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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
New contributions to the cyclic plasticity of engineering materials
Written by leading experts in the field, this book provides an authoritative and comprehensive introduction to cyclic plasticity of metals, polymers, composites and shape memory alloys. Each chapter is devoted to fundamentals of cyclic plasticity or to one of the major classes of materials, thereby providing a wide coverage of the field.
The book deals with experimental observations on metals, composites, polymers and shape memory alloys, and the corresponding cyclic plasticity models for metals, polymers, particle reinforced metal matrix composites and shape memory alloys. Also, the thermo-mechanical coupled cyclic plasticity models are discussed for metals and shape memory alloys.
Key features:
- Provides a comprehensive introduction to cyclic plasticity
- Presents Macroscopic and microscopic observations on the ratchetting of different materials
- Establishes cyclic plasticity constitutive models for different materials.
- Analysis of cyclic plasticity in engineering structures.
This book is an important reference for students, practicing engineers and researchers who study cyclic plasticity in the areas of mechanical, civil, nuclear, and aerospace engineering as well as materials science.
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Seitenzahl: 741
Veröffentlichungsjahr: 2017
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Table of Contents
Cover
Title Page
Introduction
I.1 Monotonic Elastoplastic Deformation
I.2 Cyclic Elastoplastic Deformation
I.3 Contents of This Book
References
1 Fundamentals of Inelastic Constitutive Models
1.1 Fundamentals of Continuum Mechanics
1.2 Classical Inelastic Constitutive Models
1.3 Fundamentals of Crystal Plasticity
1.4 Fundamentals of Meso‐mechanics for Composite Materials
References
2 Cyclic Plasticity of Metals
2.1 Macroscopic Experimental Observations
2.2 Microscopic Observations of Dislocation Patterns and Their Evolutions
2.3 Micro‐mechanism of Ratchetting
2.4 Summary
References
3 Cyclic Plasticity of Metals
3.1 Macroscopic Phenomenological Constitutive Models
3.2 Physical Nature‐Based Constitutive Models
3.3 Two Applications of Cyclic Plasticity Models
3.4 Summary
References
4 Thermomechanically Coupled Cyclic Plasticity of Metallic Materials at Finite Strain
4.1 Cyclic Plasticity Model at Finite Strain
4.2 Thermomechanically Coupled Cyclic Plasticity Model at Finite Strain
4.3 Summary
References
5 Cyclic Viscoelasticity–Viscoplasticity of Polymers
5.1 Experimental Observations
5.2 Cyclic Viscoelastic Constitutive Model
5.3 Cyclic Viscoelastic–Viscoplastic Constitutive Model
5.4 Summary
References
6 Cyclic Plasticity of Particle‐Reinforced Metal Matrix Composites
6.1 Experimental Observations
6.2 Finite Element Simulations
6.3 Meso‐mechanical Time‐Independent Plasticity Model
6.4 Meso‐mechanical Time‐Dependent Plasticity Model
6.5 Summary
References
7 Thermomechanical Cyclic Deformation of Shape‐Memory Alloys
7.1 Experimental Observations
7.2 Phenomenological Constitutive Models
7.3 Crystal Plasticity‐Based Constitutive Models
7.4 Summary
References
Index
End User License Agreement
List of Tables
Chapter 03
Table 3.1 Values of all parameters used in the proposed model.
Table 3.2 Values of all parameters used in the proposed models.
Table 3.3 Values of all parameters used in the proposed model.
Table 3.4 The matrix
f
αβ
for FCC single crystals (N = H = C = 8, G = 15, S = 25).
Table 3.5 The values of material parameters used in the proposed model.
Table 3.6 The values of material parameters used in the proposed model.
Table 3.7 The values of material parameters used in the proposed model.
Table 3.8 Ductility limit of the three rail steels.
Table 3.9 Material parameters used in the SWT model.
Table 3.10 Predicted crack initiation locations.
Chapter 04
Table 4.1 Outline of the proposed model.
Table 4.2 Material parameters of SUS304 used in the proposed model.
Table 4.3 Material parameters of OFHC copper.
Table 4.4 Material parameters of SS304 stainless steel.
Table 4.5 Outline of the proposed model.
Table 4.6 Material constants used in the simplified model for 316L stainless steel.
Chapter 05
Table 5.1 Coefficients of parameter functions.
Table 5.2 Material parameters used in the proposed model.
Chapter 06
Table 6.1 Values of material parameters in the reduced model for the matrix.
Table 6.2 Material parameters in the time‐dependent model for the matrix.
Chapter 07
Table 7.1 Parameters used in the proposed model.
Table 7.2 Parameters for the proposed model.
Table 7.3 Parameters for the proposed model.
Table 7.4 Parameters for the proposed model.
Table 7.5 Parameters for the proposed model.
List of Illustrations
Chapter 01
Figure 1.1 Movement of a continua body.
Figure 1.2 Dislocation slipping on a single slip system of a cylindrical single crystal.
Figure 1.3 RVE for Eshelby’s equivalence from an inhomogeneous inclusion to a homogeneous inclusion with an eigenstrain of
ε
*
. (a) RVE with an inhomogeneous inclusion and (b) RVE with an equivalent homogeneous inclusion.
Figure 1.4 The RVE for Mori–Tanaka’s approach. (a) An inclusion in the composite and (b) an inclusion in the matrix subjected to the average strain.
Chapter 02
Figure 2.1 Curve of tensile peak stress versus number of cycles with various applied strain amplitudes
ε
a
(i.e., 0.5, 1.0, 2.0, 3.0, and 4.0%) for SUS304 stainless steel.
Figure 2.2 Curve of responding stress amplitude
σ
a
versus number of cycles with two applied strain amplitudes
ε
a
(i.e., 0.6 and 0.8%) for tempered 42CrMo steel.
Figure 2.3 Curve of responding stress amplitude
σ
a
versus number of cycles with various applied strain amplitudes ε
a
(i.e., 0.5, 0.6, 0.7, and 0.8%) for annealed 42CrMo steel.
Figure 2.4 Diagrams of triangle load‐wave for multistep cyclic loading. (a) Varied strain amplitude and (b) varied mean strain.
Figure 2.5 Results of cyclic stress–strain responses in the multistep cyclic test with varied strain amplitude (i.e., (i) 0.2% (50c) → (ii) 0.4% (30c) → (iii) 0.6% (30c) → (iv) 0.8% (30c) → (v) 0.6% (20c) → (vi) 0.4% (20c), where c represents the number of cycles). (a) Cyclic stress–strain curves, (b) curves of responding stress amplitude
σ
a
versus number of cycles.
Figure 2.6 Curves of responding stress amplitude
σ
a
versus number of cycles. (a) Annealed 42CrMo steel and (b) tempered 42CrMo steel.
Figure 2.7 Curve of responding stress amplitude
σ
a
versus number of cycles obtained in the multistep cyclic test of SS304 stainless steel with a constant applied strain amplitude
ε
a
= 0.6% and varied mean strain (i.e., (i) 0.0% (20c) → (ii) 0.2% (20c) → (iii) 0.4% (20c) → (iv) 0.6% (20c) → (v) 0.2% (20c) → (vi) 0.6% (20c)).
Figure 2.8 Curve of responding stress amplitude
σ
a
versus number of cycles obtained in the multistep cyclic test with a constant applied strain amplitude
ε
a
= 0.5% and varied mean strain (i.e., (i) 0.0% (200c) → (ii) 1.0% (200c) → (iii) 2.0% (200c) → (iv) 0.0% (200c or 50c)). (a) Annealed 42CrMo steel and (b) tempered 42CrMo steel.
Figure 2.9 Curves of responding stress amplitude
σ
a
versus number of cycles in the multistep cyclic test of SS304 stainless steel with varied strain amplitude (i.e., (i) 0.2% (50c) → (ii) 0.4% (30c) → (iii) 0.6% (30c) → (iv) 0.8% (30c) → (v) 0.6% (20c) → (vi) 0.4% (20c)) and at various temperatures. (a) 200°C, (b) 400°C, and (c) 600°C.
Figure 2.10 Typical multiaxial loading paths. (a) 45° linear path, (b) 135° linear path, (c) rhombic path, (d) circular path, (e) square (or rectangle) path, and (f) butterfly‐typed path.
Figure 2.11 Cyclic stress–strain curves of SS304 stainless steel with the circular path (a) and curves of responding equivalent stress amplitude
versus number of cycles (b).
Figure 2.12 Curves of responding equivalent stress amplitude
versus number of cycles for the annealed 42CrMo steel. (a) Uniaxial and proportional multiaxial paths and (b) uniaxial and nonproportional multiaxial paths.
Figure 2.13 Curves of responding equivalent stress amplitude
versus number of cycles for the tempered 42CrMo steel. (a) Uniaxial and proportional multiaxial paths and (b) uniaxial and nonproportional multiaxial paths.
Figure 2.14 Curves of responding axial and torsional stress amplitudes versus number of cycles obtained in the multistep multiaxial cyclic test with circular path and at room temperature. (a) For SS304 stainless steel and (b) for annealed U71Mn rail steel.
Figure 2.15 Diagram of triangle load‐wave for single‐step stress‐controlled cyclic loading.
Figure 2.16 Results of uniaxial ratchetting for SS304 stainless steel in the single‐step stress‐controlled cyclic test with constant stress amplitude and various mean stresses. (a) Cyclic stress–strain curves and (b) curves of ratchetting strain
ε
r
versus number of cycles.
Figure 2.17 Curves of ratchetting strain
ε
r
versus number of cycles for SS304 stainless steel in the single‐step stress‐controlled cyclic test with constant mean stress and various stress amplitudes.
Figure 2.18 Curves of ratchetting strain
ε
r
versus number of cycles for the annealed 42CrMo steel in the single‐step stress‐controlled cyclic tests. (a) With constant stress amplitude and various mean stresses and (b) with constant mean stress and various stress amplitudes.
Figure 2.19 Curves of ratchetting strain
ε
r
versus number of cycles for the tempered 42CrMo steel in the single‐step stress‐controlled cyclic test with the loading case of 200 ± 800 MPa.
Figure 2.20 Curves of ratchetting strain
ε
r
versus number of cycles for the tempered 42CrMo steel in the single‐step stress‐controlled cyclic tests. (a) With constant stress amplitude of 700 MPa and various mean stresses and (b) with constant mean stress of 50 MPa and two stress amplitudes.
Figure 2.21 Results of uniaxial ratchetting for SS304 stainless steel in the multistep stress‐controlled cyclic test with the loading history of 78 ± 248 (50c) → 117 ± 248 (50c) → 78 ± 248 MPa (20c). (a) Cyclic stress–strain curves and (b) curves of ratchetting strain
ε
r
versus number of cycles.
Figure 2.22 Curves of ratchetting strain
ε
r
versus number of cycles for U71Mn rail steel in the stress‐controlled cyclic tests with or without previous strain‐controlled cyclic test of ±0.8% (20c).
Figure 2.23 Results of uniaxial ratchetting for SS304 stainless steel in the multistep stress‐controlled cyclic test at 200°C. (a) Cyclic stress–strain curves and (b) curves of ratchetting strain
ε
r
versus number of cycles.
Figure 2.24 Results of uniaxial ratchetting for SS304 stainless steel in the multistep stress‐controlled cyclic test at 400°C. (a) Cyclic stress–strain curves and (b) curves of ratchetting strain
ε
r
versus number of cycles.
Figure 2.25 Results of uniaxial ratchetting for SS304 stainless steel in the multistep stress‐controlled cyclic test at 600°C. (a) Cyclic stress–strain curves and (b) curves of ratchetting strain
ε
r
versus number of cycles.
Figure 2.26 Results of uniaxial ratchetting for SS304 stainless steel at different stress rates and room temperature, with a stress level of 78 ± 234 MPa. (a) Cyclic stress–strain curves at a stress rate of 13 MPa/s and (b) curves of ratchetting strain
ε
r
versus number of cycles.
Figure 2.27 Results of uniaxial ratchetting for SS304 stainless steel with or without peak/valley stress holds and at room temperature and a stress rate of 2.6 MPa/s. (a) Cyclic stress–strain curves with peak/valley stress hold for 10 s and (b) curves of ratchetting strain
ε
r
versus number of cycles.
Figure 2.28 Curves of ratchetting strain
ε
r
versus number of cycles for SS304 stainless steel with peak/valley or only peak stress holds and at a stress rate of 2.6 MPa/s.
Figure 2.29 Results of uniaxial ratchetting for SS304 stainless steel at different stress rates and 700°C, with a stress level of 40 ± 100 MPa. (a) Cyclic stress–strain curves at a stress rate of 10 MPa/s and (b) curves of ratchetting strain
ε
r
versus number of cycles.
Figure 2.30 Results of uniaxial ratchetting for SS304 stainless steel with or without peak/valley stress holds and at 700°C and a stress rate of 10 MPa/s. (a) Cyclic stress–strain curves with peak/valley stress hold for 10 s and (b) curves of ratchetting strain
ε
r
versus number of cycles.
Figure 2.31 Typical multiaxial stress‐controlled loading paths for SS304 stainless steel. (a) Linear I, (b) linear II, (c) circular, (d) elliptical, (e) rhombic, and (f) 1/2 rhombic.
Figure 2.32 Results of multiaxial ratchetting for SS304 stainless steel with linear I path and at room temperature. (a) Curves of axial strain versus equivalent shear strain and (b) curves of ratchetting strain
ε
r
versus number of cycles.
Figure 2.33 Results of multiaxial ratchetting for SS304 stainless steel with linear II path and at room temperature. (a) Curves of axial strain versus equivalent shear strain and (b) curves of ratchetting strain
ε
r
versus number of cycles.
Figure 2.34 Results of multiaxial ratchetting for SS304 stainless steel with the circular and elliptical paths and at room temperature. (a) Curves of axial strain versus equivalent shear strain with the circular path and (b) curves of ratchetting strain
ε
r
versus number of cycles.
Figure 2.35 Results of multiaxial ratchetting for SS304 stainless steel with the rhombic and 1/2 rhombic paths and at room temperature. (a) Curves of axial strain versus equivalent shear strain with the rhombic path and (b) curves of ratchetting strain
ε
r
versus number of cycles.
Figure 2.36 Multiaxial circular stress‐controlled loading path and its inscribed paths (i.e., with the same maximum equivalent stress) for the annealed 42CrMo steel. (a) 90° linear, (b) 45° linear, (c) 135° linear, (d) square, (e) rhombic, and (f) butterfly‐typed.
Figure 2.37 Results of multiaxial ratchetting for the annealed 42CrMo steel with circular and its inscribed paths and at room temperature.
Figure 2.38 Results of multiaxial ratchetting for the annealed 42CrMo steel with circular and rhombic paths and different axial mean stresses (both the axial and equivalent shear stress amplitudes are ±350 MPa) and at room temperature. (a) With the rhombic path and various axial mean stresses and (b) with the rhombic and circular paths and various axial mean stresses.
Figure 2.39 Two new multiaxial stress‐controlled loading paths for the tempered 42CrMo steel. (a) Square and (b) butterfly‐typed.
Figure 2.40 Results of multiaxial ratchetting for the tempered 42CrMo steel with various paths. (a) With the rhombic and circular paths and various axial mean stresses (both the axial and equivalent shear stress amplitudes are ±750 MPa) and (b) with various loading paths with the same axial mean stress of 100 MPa.
Figure 2.41 Results of multiaxial ratchetting for the tempered 42CrMo steel with circular and rhombic paths and at different stress levels and at room temperature. (a) With the rhombic path and various axial mean stresses (both the axial and equivalent shear stress amplitudes are ±750 MPa) and (b) with the circular path and various stress amplitudes (the axial and equivalent shear stress amplitudes are the same and the axial mean stress is 100 MPa).
Figure 2.42 Results of multiaxial ratchetting for SS304 stainless steel with linear II path and at different temperatures. (a) Curves of axial strain versus equivalent shear strain at 200°C, (b) curves of axial strain versus equivalent shear strain at 600°C, (c) curves of axial ratchetting strain versus number of cycles, and (d) curves of torsional ratchetting strain versus number of cycles.
Figure 2.43 Results of multiaxial ratchetting for SS304 stainless steel with other paths and at 600°C. (a) Curves of axial strain versus equivalent shear strain with the circular path and (b) curves of ratchetting strain versus number of cycles.
Figure 2.44 Three kinds of multiaxial stress‐controlled loading paths for SS304 stainless steel. (a) 90° linear path, (b) rhombic path, and (c) circular path.
Figure 2.45 Results of multiaxial ratchetting for SS304 stainless steel with the 90° linear path, at different stress rates and room temperature. (a) Curves of axial strain versus shear strain at 100 MPa/s and (b) curves of axial ratchetting strain versus number of cycles.
Figure 2.46 Results of multiaxial ratchetting for SS304 stainless steel with the 90° linear path, with or without peak/valley stress hold and at room temperature and 10 MPa/. (a) Curves of axial strain versus shear strain without any hold and (b) curves of axial ratchetting strain versus number of cycles.
Figure 2.47 Results of multiaxial ratchetting for SS304 stainless steel with the 90° linear path and at 700°C. (a) Curves of axial ratchetting strain versus number of cycles at various stress rates and (b) curves of axial ratchetting strain versus number of cycles with or without peak/valley stress hold.
Figure 2.48 Results of multiaxial ratchetting for SS304 stainless steel with the rhombic and circular paths (with equivalent shear stress amplitude of ±234 MPa and zero mean shear stress; axial stress amplitude of ±234 MPa and axial mean stress of 78 MPa), at different stress rates and room temperature. (a) Curves of axial strain versus shear strain for the rhombic path, at 20 MPa/s and (b) curves of axial ratchetting strain versus number of cycles.
Figure 2.49 Results of multiaxial ratchetting for SS304 stainless steel with the rhombic path (with equivalent shear stress amplitude of ±100 MPa and zero mean shear stress; axial stress amplitude of ±100 MPa and axial mean stress of 40 MPa), at different stress rates and room temperature. (a) Curves of axial strain versus shear strain at 40 MPa/s and (b) curves of axial ratchetting strain versus number of cycles.
Figure 2.50 Tensile stress–strain curves of SS316L stainless steel obtained with different maximum tensile strains.
Figure 2.51 Results of cyclic stress–strain responses for SS316L stainless steel in the strain‐controlled cyclic tests with a strain amplitude of ±0.7% and different numbers of cycles (50 and 1000c). (a) Curves of strain versus stress and (b) curves of stress amplitude versus number of cycles.
Figure 2.52 Ratchetting of SS316L stainless steel obtained in the stress‐controlled cyclic tests with a stress level of 70 ± 350 MPa and different numbers of cycles (50, 1000, and 2100c). (a) Curves of strain versus stress and (b) curves of ratchetting strain versus number of cycles.
Figure 2.53 TEM micrographs of SS316L stainless steel after solution treatment. (a) Trigeminal grain boundary (assigned by the arrow) and dislocation lines and (b) dislocation lines and dislocation pileup (assigned by the arrow).
Figure 2.54 Typical dislocation patterns observed in the monotonic tension of SS316L stainless steel. (a) Dislocation lines, (b) dislocation tangles, (c) dislocation cells and heavy tangles, and (d) twins in two directions.
Figure 2.55 Typical dislocation patterns observed in the strain‐controlled cyclic deformation of SS316L stainless steel. (a) Dislocation tangles, (b) incipient dislocation cells, (c) dislocation walls, and (d) medium‐staged dislocation cells.
Figure 2.56 Typical dislocation patterns observed in the ratchetting deformation of SS316L stainless steel. (a) Dislocation tangles, (b) dislocation lines and tangles near grain boundary, (c) dislocation veins, (d) dislocation walls and incipient cells, (e) early dislocation cells, and (f) polarized dislocation cells.
Figure 2.57 Loading paths used in the multiaxial strain‐controlled cyclic tests. (a) Pure torsion, (b) 45° linear, (c) rhombic, and (d) circular.
Figure 2.58 Loading paths used in the multiaxial stress‐controlled cyclic tests. (a) Circular, (b) 45° linear, (c) rhombic, and (d) butterfly‐typed.
Figure 2.59 Experimental results of responding stress amplitude versus number of cycles for four strain‐controlled loading paths.
Figure 2.60 Curves of axial ratchetting strain versus number of cycles with various loading paths. (a) 30° linear path, (b) rhombic path, (c) circular path, and (d) butterfly‐typed path.
Figure 2.61 Typical dislocation patterns observed in the multiaxial strain‐controlled cyclic deformation of SS316L stainless steel. (a) Thick dislocation walls with tendency to form cells, (b) fine twin strips (assigned by the white arrows) and dislocation walls, (c) dislocation walls, and (d) incipient dislocation cells.
Figure 2.62 Typical dislocation patterns observed in the multiaxial ratchetting deformation of SS316L stainless steel with 30° linear path. (a) Dislocation network and dislocation dipole (assigned by the rectangle), (b) dislocation tangles, (c) aligned dislocation arrays and heavy dislocation tangles, and (d) dislocation walls with tendency to form cells.
Figure 2.63 Typical dislocation patterns observed in the multiaxial ratchetting deformation of SS316L stainless steel with other paths. (a) Dislocation tangles with the trace of multiple slip, (b) heavy dislocation tangles with tendency to form cells, (c) incipient dislocation cells, and (d) fine twin strips.
Figure 2.64 Monotonic tensile stress–strain curves of 20 carbon steel with different prescribed axial strains.
Figure 2.65 Curves of responding stress amplitude versus number of cycles for the strain‐controlled cyclic tension–compression tests of 20 carbon steel with the same strain amplitude but different numbers of cycles.
Figure 2.66 Curves of ratchetting strain versus number of cycles for the stress‐controlled cyclic tension–compression tests of 20 carbon steel with the same stress level (50 ± 275 MPa) but different prescribed numbers of cycles, where ratchetting strain
ε
r
= 0.0 before about 125 cycles.
Figure 2.67 TEM micrographs of original normalized 20 carbon steel. (a) Grain with very few dislocation lines and (b) dislocation lines near the grain boundary (assigned by the arrow).
Figure 2.68 Typical dislocation patterns observed in the monotonic tension of 20 carbon steel. (a) Dislocation tangles and dislocation veins, (b) incipient cells (assigned by arrow), (c) newly formed aligned dislocation lines between the veins and inside the cells, (d) incipient sub‐grains, and (e) sub‐grains.
Figure 2.69 Typical dislocation patterns observed in the strain‐controlled cyclic deformation of 20 carbon steel. (a) Dislocation veins and tangles, (b) dislocation tangles and incipient cells, (c) dislocation walls and cells, and (d) heavy dislocation tangles and cells.
Figure 2.70 Typical dislocation patterns observed in the ratchetting deformation of 20 carbon steel without the pre‐strain. (a) Dislocation veins and incipient cells, (b) dislocation cells and incipient sub‐grains (assigned by arrows), (c) dislocation cells and walls, and (d) sub‐grains.
Figure 2.71 Typical dislocation patterns observed in the ratchetting deformation of 20 carbon steel with the pre‐strain. (a) Dislocation cells with thick walls (assigned by arrow), (b) dislocation walls and cells, (c) dislocation cells and sub‐grains (assigned by arrows), (d) sub‐grains, (e) crossed dislocation lines inside cell (assigned by arrow), and (f) reformed dislocation lines inside sub‐grains (assigned by arrows).
Figure 2.72 Loading paths used in the multiaxial strain‐controlled cyclic tests. (a) Pure torsion, (b) 45° linear, (c) butterfly‐typed, and (d) circular.
Figure 2.73 Loading paths used in the multiaxial stress‐controlled cyclic tests. (a) Uniaxial, (b) circular, (c) 45° linear, (d) butterfly‐typed, (e) rhombic, (f) square, (g) cross, and (h) X‐typed.
Figure 2.74 Experimental results of responding stress amplitude versus number of cycles for four strain‐controlled loading paths.
Figure 2.75 Curves of axial ratchetting strain versus number of cycles for 20 carbon steel in multiaxial stress‐controlled cyclic tests with the same stress levels and various loading paths. (a) For uniaxial, circular, rhombic, and cross paths and (b) for butterfly‐typed, square, 45° linear, and X‐typed paths.
Figure 2.76 Curves of axial ratchetting strain versus number of cycles for 20 carbon steel in the multiaxial stress‐controlled cyclic tests with different cyclic numbers and various loading paths. (a) With the inscribed 45° linear path and (b) with the circular path.
Figure 2.77 Typical dislocation patterns observed in the multiaxial ratchetting deformation of 20 carbon steel at different stages and with the proportional 45° linear path. (a) Dislocation tangles, (b) dissolved dislocation tangles tending to form cells, (c) dislocation cells and incipient sub‐grains, (d) dislocation walls, (e) sub‐grains and cells, and (f) dislocation tangles.
Figure 2.78 Typical dislocation patterns observed in the multiaxial ratchetting deformation of 20 carbon steel at different stages and with the nonproportional circular path. (a) Incipient cells, (b) dislocation cells, (c) dislocation cells and incipient sub‐grains, and (d) sub‐grains.
Figure 2.79 Typical dislocation patterns observed in the multiaxial ratchetting deformation of 20 carbon steel with inscribed cross and butterfly‐typed paths after 1000 cycles. (a) Dislocation cells, (b) dislocation cells and incipient sub‐grains, (c) sub‐grains, and (d) sub‐grains and reformed dislocation lines inside the sub‐grains.
Figure 2.80 Typical dislocation patterns of SS316L stainless steel at 1/4 cycle during the ratchetting test with a peak stress of 420 MPa and valley stress of −280 MPa. (a) Dislocation lines and light dislocation tangles and (b) heavy dislocation tangles and incipient walls.
Figure 2.81 Typical dislocation patterns of SS316L stainless steel at 3/4 cycle during the ratchetting test with a peak stress of 420 MPa and valley stress of −280 MPa. (a) Dissolved light dislocation tangles and (b) dissolved heavy dislocation tangles and incipient walls.
Chapter 03
Figure 3.1 Experimental monotonic tensile plastic strain–stress curve used to determine the material parameters
ζ
i
and
r
i
.
Figure 3.2 Experimental and predicted uniaxial ratchetting of SS304 stainless steel with 78 ± 248 MPa: (a) experimental data; (b) simulated by Ohno–Wang’s model II with the isotropic hardening rule; (c) simulated only by the Ohno–Wang model II; (d) simulated only by the Ohno–Wang model I.
Figure 3.3 Experimental and predicted multiaxial ratchetting of SS304 stainless steel with linear path: (a) experimental data; (b) simulated by Ohno–Wang’s model II with the isotropic hardening rule; (c) simulated only by the Ohno–Wang model II; (d) simulated only by the Ohno–Wang model I; (e) simulated only by the Ohno–Wang model I with the isotropic hardening rule.
Figure 3.4 Curves of responding peak stress versus the number of cycles obtained in the symmetrical uniaxial strain‐controlled cyclic loading tests of SS304 stainless steel with different applied strain ranges.
Figure 3.5 Experimental and predicted unsaturated cyclic hardening of SS304 stainless steel.
Figure 3.6 Experimental curve of
σ
max
versus
p
.
Figure 3.7 Original stress–plastic strain (
σ–ε
p
) and modified stress–plastic strain (
σ
*
–
ε
p
) curves.
Figure 3.8 Experimental and simulated monotonic tensile stress–strain curves of SS304 stainless steel at various temperatures.
Figure 3.9 Experimental (a) and predicted (b) uniaxial ratchetting of SS304 stainless steel at room temperature.
Figure 3.10 Experimental (a) and predicted (b) uniaxial ratchetting of SS304 stainless steel at 200°C.
Figure 3.11 Experimental (a) and predicted (b) uniaxial ratchetting of SS304 stainless steel at 400°C.
Figure 3.12 Experimental (a) and predicted (b) uniaxial ratchetting of SS304 stainless steel at 600°C.
Figure 3.13 Experimental (a) and predicted (b) multiaxial ratchetting of SS304 stainless steel with the linear path and at room temperature.
Figure 3.14 Experimental (a) and predicted (b) multiaxial ratchetting of SS304 stainless steel with the linear path and at 200°C.
Figure 3.15 Experimental (a) and predicted (b) multiaxial ratchetting of SS304 stainless steel with the linear path and at 400°C.
Figure 3.16 Experimental (a) and predicted (b) multiaxial ratchetting of SS304 stainless steel with the linear path and at 600°C.
Figure 3.17 Experimental (a) and predicted (b) multiaxial ratchetting of SS304 stainless steel with the circular path and at room temperature.
Figure 3.18 Experimental (a) and predicted (b) multiaxial ratchetting of SS304 stainless steel with the circular path and at 600°C.
Figure 3.19 Monotonic tensile stress–strain curves of experiments and simulations: (a) and (b) at room temperature; (c) and (d) at 700°C.
Figure 3.20 Uniaxial ratchetting of SS304 stainless steel at different stress rates and at room temperature: (a) experimental stress–strain curve at a stress rate of 13 MPa/s; (b) simulated stress–strain curve at a stress rate of 13 MPa/s by the SVC model; (c) ratchetting strain
ε
r
versus the number of cycles
N
at three stress rates with the simulations by the UVP and SPC models; (d) ratchetting strain
ε
r
versus the number of cycles
N
at three stress rates with the simulations by the SVC model.
Figure 3.21 Uniaxial ratchetting of SS304 stainless steel with or without peak/valley stress hold and at a stress rate of 2.6 MPa/s and room temperature: (a) experimental stress–strain curve with a hold time of 10 s; (b) simulated stress–strain curve with a hold time of 10 s by the SVC model; (c) ratchetting strain
ε
r
versus the number of cycles
N
with different hold times and the simulations by the UVP and SPC models; (d) ratchetting strain
ε
r
versus the number of cycles
N
with different hold times and the simulations by the SVC model.
Figure 3.22 Uniaxial ratchetting of SS304 stainless steel at different stress rates and at 700°C: (a) experimental stress–strain curve at a stress rate of 10 MPa/s; (b) simulated stress–strain curve at a stress rate of 10 MPa/s by the SVC model; (c) ratchetting strain
ε
r
versus the number of cycles
N
at three stress rates with the simulations by the UVP and SPC models; (d) ratchetting strain
ε
r
versus the number of cycles
N
at three stress rates with the simulations by the SVC model.
Figure 3.23 Uniaxial ratchetting of SS304 stainless steel with or without peak/valley stress hold and at a stress rate of 10 MPa/s and 700°C: (a) experimental stress–strain curve with a hold time of 10 s; (b) simulated stress–strain curve with a hold time of 10 s by the SVC model; (c) ratchetting strain
ε
r
versus the number of cycles
N
with different hold times and the simulations by the UVP and SPC models; (d) ratchetting strain
ε
r
versus the number of cycles
N
with different hold times and the simulations by the SVC model.
Figure 3.24 Uniaxial ratchetting of SS304 stainless steel: (a) at room temperature and different stress rates; (b) at room temperature and with different hold times; (c) at 700°C and different stress rates; (d) at 700°C and with different hold times.
Figure 3.25 Change of residual radial displacement on the middle surface of hollow cylinder with the increasing number of cycles. (a) PP model, (b) LKH model, (c) A–F model, and (d) O–W model.
Figure 3.26 Monotonic tensile stress–strain curves.
Figure 3.27 Evolution curves of resolved shear stress amplitude.
Figure 3.28 Simulated ratchetting of copper single crystal in the direction of single slip.
Figure 3.29 Monotonic tensile stress–strain curves of 316L stainless steel.
Figure 3.30 Simulated and experimental cyclic stress–strain responses of 316L stainless steel in the uniaxial strain‐controlled cyclic test with a strain amplitude of 0.7%: (a) experimental cyclic stress–strain curves; (b) simulated cyclic stress–strain curves; (c) results of responded stress amplitude versus the number of cycles.
Figure 3.31 Simulated and experimental ratchetting of 316L stainless steel: (a) experimental cyclic stress–strain curves (70 ± 330 MPa); (b) simulated cyclic stress–strain curves (70 ± 330 MPa); (c) curves of ratchetting strain versus the number of cycles with varied stress amplitude (
σ
m
= 70 MPa); (d) curves of ratchetting strain versus the number of cycles with varied mean stress (
σ
a
= 350 MPa).
Figure 3.32 Simulated multiaxial ratchetting of polycrystalline 316L stainless steel for the rhombic and 1/2 rhombic loading paths: asymmetrical axial cyclic stressing with an axial mean stress of 70 MPa and stress amplitude of ±350 MPa and symmetrical torsional cyclic stressing with the equivalent shear stress amplitudes of ±350 and ±175 MPa, respectively.
Figure 3.33 Predicted ratchetting of 316L single crystal in the direction of [0 0 1]: (a) cyclic stress–strain curves; (b) curves of ratchetting strain versus the number of cycles.
Figure 3.34 Predicted curves of ratchetting strain versus the number of cycles for 316L single crystal in the direction of [0 0 1] with different stress levels.
Figure 3.35 Predicted curves of ratchetting strain versus the number of cycles for 316L single crystal in the different directions.
Figure 3.36 Monotonic tensile stress–strain curves of polycrystalline 316L stainless steel.
Figure 3.37 Experimental and predicted cyclic stress–strain responses of polycrystalline 316L stainless steel in the uniaxial strain‐controlled cyclic test with a strain amplitude of ±0.7%: (a) experimental cyclic stress–strain curves; (b) predicted cyclic stress–strain curves; (c) results of responding stress amplitude versus the number of cycles.
Figure 3.38 Predicted and experimental uniaxial ratchetting of polycrystalline 316L stainless steel: (a) experimental cyclic stress–strain curves (70 ± 330 MPa); (b) simulated cyclic stress–strain curves (70 ± 330 MPa); (c) curves of ratchetting strain versus the number of cycles with various stress amplitudes; (d) curves of ratchetting strain versus the number of cycles with various mean stresses; (e) curves of mean dislocation density versus the number of cycles in various loading cases.
Figure 3.39 Comparison of uniaxial ratchetting results obtained in the loading case of 70 ± 350 MPa by the tests using uniaxial solid‐bar and multiaxial tubular specimens, respectively, and the corresponding predictions.
Figure 3.40 Experimental and simulated results of multiaxial ratchetting with different loading paths: (a) and (b) curves of axial strain versus torsional strain with 30° linear path; (c) and (d) curves of axial strain versus torsional strain with rhombic path; (e) and (f) curves of axial strain versus torsional strain with circular path; (g) curves of axial ratchetting strain versus the number of cycles
N
with three multiaxial loading paths; (h) curves of mean dislocation density versus the number of cycles with three multiaxial loading paths.
Figure 3.41 Loading paths for biaxial compressive–torsional stress‐controlled cyclic tests. (a) Linear path, (b) oblique path, (c) rectangular path, (d) butterfly path, and (e) elliptical path.
Figure 3.42 Diagram of stress amplitude
σ
a
versus the number of cycles
N
of all the three rail steels under uniaxial symmetrical strain cycling with strain amplitude of 0.8%.
Figure 3.43 Experimental results of equivalent shear stress versus axial strain of the three studied rail steels during 1st and 100th cycles under (a) linear, (b) oblique, (c) rectangular, (d) butterfly, and (e) elliptical paths with the same loading condition of (
σ
eq
)
a
= 1019.8 MPa.
Figure 3.44 (a) Finite element model; and (b) finite element mesh in the contact region for simulating wheel–rail cyclic rolling contact.
Figure 3.45 Schematic illustration of the moving contact load distributions on the rail head in a loading cycle.
Figure 3.46 Maximum ratchetting strain rate versus the number of cycles
N
with different values of normalized tangential traction
ξ
for (a) LAHT steel; (b) HE1 steel; and (c) HE2 steel, with an axle load
L
of 35 tonnes and friction coefficient
f
of 0.4.
Figure 3.47 Stabilized maximum ratchetting strain rate versus the normalized tangential traction
ξ
for all the three rail steels with an axle load
L
of 35 tonnes and friction coefficient
f
of 0.4.
Figure 3.48 Estimated crack initiation life
N
i
versus normalized tangential traction
ξ
for all the three rail steels with an axle load
L
of 35 tonnes and friction coefficient
f
of 0.4.
Figure 3.49 3D mesh and loading conditions for the test specimen of bending fretting fatigue.
Figure 3.50 2D mesh and loading conditions for the test specimen of bending fretting fatigue.
Figure 3.51 Distributions of peak total strain components along the path 2 (model A) in the 100th cycle: (a)
ε
x
, (b)
ε
y
, and (c)
γ
xy
.
Figure 3.52 Distributions of peak total strain components along the path 2 by using model A: (a)
ε
x
, (b)
ε
y
, and (c)
γ
xy
.
Figure 3.53 Ratchetting during the bending fretting by using model A: (a)
ε
x
, (b)
ε
y
, and (c)
γ
xy
.
Figure 3.54 Distributions of peak total strain components along the path 2 by using model B: (a)
ε
x
, (b)
ε
y
, and (c)
γ
xy
.
Figure 3.55 Distributions of SWT parameter along path 2: (a) for model A; (b) for model B.
Figure 3.56 Predicted results of bending fretting fatigue life: (a) by model A; (b) by model B.
Chapter 04
Figure 4.1 Simulated and experimental results of shear stress and axial stress versus shear strain for the monotonic simple shear deformation of SUS304 stainless steel at finite stain.
Figure 4.2 Finite element model of free‐end tubular torsion.
Figure 4.3 Experimental (a) and simulated (b) stress–strain curves obtained in the case of CT‐1.
Figure 4.4 Experimental (a) and simulated (b) stress–strain curves obtained in the case of CT‐2.
Figure 4.5 Experimental (a) and simulated (b) shear strain–axial strain responses obtained in the case of CT‐2.
Figure 4.6 Experimental (a) and simulated (b) curves of axial strain versus shear strain in the case of FLC‐1.
Figure 4.7 Experimental (a) and simulated (b) curves of axial strain versus shear strain in the case of FLC‐2.
Figure 4.8 Experimental (a) and simulated (b) curves of axial strain versus shear strain in the case of FLC‐3.
Figure 4.9 Experimental and simulated evolution curves of axial peak strain versus number of cycles: (a) in the case of SLC and (b) in the case of TLC.
Figure 4.10 Curves of ratchetting strain versus number of cycles: (a) with various mean stresses and (b) with various stress amplitudes.
Figure 4.11 One‐dimensional rheological model for elasto‐viscoplasticity considering combined nonlinear kinematic hardening and isotropic hardening.
Figure 4.12 Geometry of simplified finite element model.
Figure 4.13 Experimental (a) and predicted (b) axial true stress–Hencky’s strain curves of 316L stainless steel in monotonic tensile tests at varied strain rates.
Figure 4.14 Experimental (a) and predicted (b) temperature rise–axial Hencky’s strain curves of 316L stainless steel in monotonic tensile tests at varied strain rates.
Figure 4.15 Experimental (a) and predicted (b) curves of stress and temperature rise versus axial Hencky’s strain in monotonic tensile tests of 316L stainless steel at a strain rate of 2 × 10
−2
s
−1
.
Figure 4.16 Experimental and simulated distribution of temperature rise for 316L stainless steel (along the path AC, defined in Figure 4.12) at different stages of tensile test with varied nominal strain
e
and at a strain rate of 2 × 10
−2
s
−1
.
Figure 4.17 Experimental and simulated results of axial true stress amplitude versus number of cycles in the uniaxial strain‐controlled cyclic test at a strain rate of 5 × 10
−3
s
−1
.
Figure 4.18 Experimental (a) and predicted (b) curves of temperature rise versus normalized time in the uniaxial strain‐controlled cyclic test at a strain rate of 5 × 10
−3
s
−1
.
Figure 4.19 Typical thermomechanical responses of 316L stainless steel in a uniaxial symmetric strain‐controlled cyclic test for the first and second cycles (with a nominal strain amplitude of 0.8% and at a strain rate of 5 × 10
−3
s
−1
): (a) experiment; (b) simulation.
Figure 4.20 Experimental (a) and simulated (b) curves of temperature rise versus normalized time in the uniaxial strain‐controlled cyclic tests at various strain rates and with a strain amplitude of 0.8%.
Figure 4.21 Experimental and simulated distributions of temperature rise along the axial direction of specimen at some specific normalized time in the uniaxial strain‐controlled cyclic tests at various strain rates and with a strain amplitude of 0.8%.
Figure 4.22 Experimental and simulated ratchetting obtained in the cases with a constant stress amplitude of 360 MPa and various mean stresses, that is, 10, 30, and 50 MPa: (a) experimental true stress–Hencky’s strain loops (with a mean stress of 30 MPa); (b) simulated true stress–Hencky’s strain loops (with a mean stress of 30 MPa); (c) ratchetting strain versus number of cycles.
Figure 4.23 Experimental and simulated ratchetting strain versus number of cycles obtained in the cases with a constant mean stress of 30 MPa and various stress amplitudes, that is, 320, 340, and 360 MPa.
Figure 4.24 Experimental and simulated ratchetting strain versus number of cycles of 316L stainless steel obtained in the multistep cyclic test with the same stress level (i.e., a stress amplitude of 360 MPa and a mean stress of 30 MPa) but at various stress rates, that is, from 100 to 250 and then 400 MPa/s.
Figure 4.25 Experimental (a) and simulated (b) curves of temperature rise versus normalized time in the cases with a constant stress amplitude of 360 MPa and various mean stresses, that is, 10, 30, and 50 MPa.
Figure 4.26 Experimental (a) and simulated (b) curves of temperature rise versus normalized time in the cases with a constant mean stress of 30 MPa and various stress amplitudes, that is, 320, 340, and 360 MPa.
Figure 4.27 Experimental and simulated results of temperature rise versus normalized time obtained in the multistep cyclic test with the same stress level (i.e., a stress amplitude of 360 MPa and a mean stress of 30 MPa) but at various stress rates, that is, from 100 to 250 and then 400 MPa/s.
Figure 4.28 Typical thermomechanical responses of 316L stainless steel in a uniaxial asymmetric stress‐controlled cyclic test for the first and second cycles (with a stress amplitude of 360 MPa and a mean stress of 30 MPa and at a stress rate of 250 MPa/s): (a) experiment; (b) simulation.
Chapter 05
Figure 5.1 Tensile results of the PC polymer at various temperatures and a strain rate of 0.0005 s
−1
: (a) engineering stress–strain curves; (b) the PRRS versus hold time at two temperatures.
Figure 5.2 Tensile stress–strain curves of the PC at various strain rates (0.025 and 0.0005 s
−1
).
Figure 5.3 Results of strain‐controlled cyclic tests for the PC with various applied strain amplitudes
ε
a
(i.e., 2.0, 2.5, and 3.0%) at a strain rate of 0.001 s
−1
and at room temperature: (a) stress–strain hysteresis loops with the strain amplitude of 3.0%; (b) curves of responding stress amplitude
σ
a
versus the number of cycles.
Figure 5.4 Curve of responding stress amplitude
σ
a
versus the number of cycles for the PC with a history of applied strain amplitude
ε
a
(i.e., 2.5 → 3.0 → 2.5%) at a strain rate of 0.005 s
−1
and at room temperature.
Figure 5.5 Curve of responding stress amplitude
σ
a
versus the number of cycles for the PC with a strain amplitude
ε
a
of 2.0% at a strain rate of 0.001 s
−1
and at different temperatures.
Figure 5.6 Stress–strain curves of the PC obtained in the monotonic tensile and torsional tests at different loading rates.
Figure 5.7 Results obtained in torsional–angle‐controlled cyclic tests: (a) cyclic stress–strain curves with torsional–angle range of ±9° and at an angle rate of 5°/s; (b) curves of equivalent shear stress amplitude versus the number of cycles in different load cases.
Figure 5.8 Cyclic stress–strain curves with hourglass‐typed path (a) and curves of responding axial stress amplitude
σ
a
(b) and equivalent shear stress amplitude 3
1/2
τ
a
(c) versus the number of cycles.
Figure 5.9 Typical multiaxial loading paths: (a) rhombic path, (b) hourglass‐typed path, and (c) butterfly‐typed path.
Figure 5.10 Results of uniaxial ratchetting for the PC in the cyclic tests with constant stress amplitude and various mean stresses: (a) cyclic stress–strain curves; (b) curves of ratchetting strain
ε
r
versus the number of cycles.
Figure 5.11 Curves of ratchetting strain
ε
r
versus the number of cycles for the PC in the cyclic test with constant mean stress and various stress amplitudes.
Figure 5.12 Results of uniaxial ratchetting for the PC in the multistepped cyclic test with the loading histories of 40 ± 10 (50c) → 50 ± 10 (50c) → 40 ± 10 MPa (50c) and 40 ± 10 (50c) → 40 ± 20 (50c) → 40 ± 10 MPa (50c): (a) cyclic stress–strain curves; (b) curves of ratchetting strain
ε
r
versus the number of cycles.
Figure 5.13 Cyclic stress–strain hysteresis loops at 0°C and with different valley stresses: (a) 0.1
σ
y
, (b) −0.1
σ
y
, (c) −0.3
σ
y
, and (d) −0.5
σ
y
.
Figure 5.14 Cyclic stress–strain hysteresis loops at 30°C and with different valley stresses: (a) 0.1
σ
y
, (b) −0.1
σ
y
, (c) −0.3
σ
y
, and (d) −0.5
σ
y
.
Figure 5.15 Cyclic stress–strain hysteresis loops at 60°C and with different valley stresses: (a) 0.1
σ
y
, (b) −0.1
σ
y
, (c) −0.3
σ
y
, and (d) −0.5
σ
y
.
Figure 5.16 Cyclic stress–strain hysteresis loops at 90°C and with different valley stresses: (a) 0.1
σ
y
, (b) −0.1
σ
y
, (c) −0.3
σ
y
, and (d) −0.5
σ
y
.
Figure 5.17 Curves of the PRSI versus the number of cycles with different valley stresses: (a) 0°C, (b) 30°C, (c) 60°C, and (d) 90°C.
Figure 5.18 Curves of the PRSI versus the number of cycles at different temperatures: (a) 0.1
σ
y
, (b) −0.1
σ
y
, (c) −0.3
σ
y
, and (d) −0.5
σ
y
.
Figure 5.19 Curves of recovery strain versus zero stress hold time for the load cases with different valley stresses and at the same temperature: (a) 0°C, (b) 30°C, and (c) 60°C.
Figure 5.20 Rate‐dependent ratchetting of the PC at two stress rates and room temperature, with a stress level of 50 ± 10 MPa: (a) cyclic stress–strain curves at stress rate of 1 MPa/s; (b) curves of ratchetting strain
ε
r
versus the number of cycles.
Figure 5.21 Time‐dependent ratchetting of the PC with or without peak stress hold and at room temperature, with a stress level of 40 ± 10 MPa: (a) cyclic stress–strain curves with peak stress hold 25 s; (b) curves of ratchetting strain
ε
r
versus the number of cycles.
Figure 5.22 Loading paths used in the pure stress‐controlled tests: (a) square, (b) rhombic, (c) butterfly‐typed, (d) hourglass, (e) torque‐hourglass, (f) linear I, and (g) linear II.
Figure 5.23 Strain responses obtained in the pure stress‐controlled multiaxial cyclic tests with the same stress level and stress rate (30 ± 28.3 MPa, 1 MPa/s) but different loading paths: (a) butterfly‐typed one and (b) torque‐hourglass one.
Figure 5.24 Curves of ratchetting strain versus the number of cycles obtained in the pure stress‐controlled multiaxial cyclic tests with the same stress level and at the same stress rate (i.e., 30 ± 28.3 MPa, 1 MPa/s) but with different loading paths.
Figure 5.25 Strain responses obtained in the stress‐controlled multiaxial cyclic test with the rhombic path and different mean stresses, with the same stress amplitude of 28.3 MPa and at the same stress rate of 1 MPa/s: (a) 30 MPa and (b) 35 MPa.
Figure 5.26 Curves of ratchetting strain versus the number of cycles obtained in the pure stress‐controlled multiaxial cyclic tests with the same stress amplitude of 28.3 MPa and at the same stress rate of 1 MP/s but with different mean stresses and loading paths: (a) rhombic, (b) butterfly‐typed, and (c) torque‐hourglass.
Figure 5.27 Curves of ratchetting strain versus the number of cycles obtained in the pure stress‐controlled multiaxial cyclic tests with the same mean stress of 30 MPa and at the same stress rate of 1 MP/s but with different stress amplitudes and loading paths: (a) rhombic, (b) hourglass, and (c) butterfly‐typed.
Figure 5.28 Curves of ratchetting strain versus the number of cycles obtained in the pure stress‐controlled multiaxial cyclic tests with the same stress level of 35 ± 28.3 MPa but at different stress rates and with different loading paths: (a) rhombic and (b) butterfly‐typed.
Figure 5.29 Results obtained with stress histories: (a) strain response with a typical stress history (i.e., with a stress amplitude of 28.3 MPa, stress rate of 1 MPa/s, and a mean stress history of 30 → 10 → 30 MPa) and (b) ratchetting strain versus the number of cycles with the butterfly‐typed path and different stress histories (i.e., mean stress history and stress amplitude one).
Figure 5.30 Results obtained in the mixed stress–strain‐controlled multiaxial cyclic tests with different axial and equivalent shear stress histories: (a) strain responses in the case with a torsional–angle range of ±5°, torsional–angle rate of 0.5°/s, and an axial stress history of 40 → 30 → 40 → 30 MPa, (b) strain responses in the case with an axial‐displacement range of ±0.3 mm, displacement rate of 0.03 mm/s, and an equivalent shear stress history of 40 → 30 → 40 → 30 MPa and (c) curves of ratchetting versus the number of cycles.
Figure 5.31 Curves of ratchetting versus the number of cycles in the tests with a torsional–angle range history (i.e., with an axial stress of 40 MPa, torsional–angle rate of 0.5°/s, and a torsional–angle range history of ±6 → ±3 → ±6 → ±3°) and axial‐displacement range history (i.e., with an equivalent shear stress of 40 MPa, axial‐displacement rate of 0.03 mm/s, and a displacement amplitude history of ±0.4 → ±0.2 → ±0.4 → ±0.2 mm).
Figure 5.32 Curves of ratchetting versus the number of cycles in the tests with a torsional–angle rate history (i.e., with an axial stress of 40 MPa, torsional–angle range of ±5°, and a torsional–angle rate history of 0.1 → 0.5 → 0.1 → 0.5°/s) and an axial‐displacement rate history (i.e., with an equivalent shear stress of 40 MPa, axial‐displacement range of ±0.3 mm, and an axial‐displacement rate history of 0.006 → 0.03 → 0.006 → 0.03 mm/s).
Figure 5.33 Tensile stress–strain curves of the PEI at different stress rates (i.e., 1, 6, and 30 MPa/s).
Figure 5.34 Experimental and simulated ratchetting in the case with a mean stress of 15 MPa and stress amplitude of 50 MPa: (a) first hysteresis loop and (b) curves of ratchetting strain versus the number of cycles.
Figure 5.35 Experimental and simulated ratchetting in the case with a mean stress of 32.5 MPa and stress amplitude of 32.5 MPa: (a) first hysteresis loop and (b) curves of ratchetting strain versus the number of cycles.
Figure 5.36 Creep and recovery curves of the PEI with a dead stress of 65 MPa and at room temperature.
Figure 5.37 Experimental and simulated stress–strain curves of the PEI for the load case with a mean stress of 15 MPa and stress amplitude of 50 MPa: (a) first hysteresis loops, (b) experimental stress–strain curves for 200 cycles, and (c) simulated stress–strain curves for 200 cycles.
Figure 5.38 Experimental and simulated curves of ratchetting strain versus the number of cycles for the PEI: (a) for the cases with same stress amplitude (50 MPa) but various mean stresses (i.e., 10, 15, and 20 MPa) at a stress rate of 30 MPa/s, (b) for the cases with same mean stress (15 MPa) but various stress amplitudes (i.e., 45, 50, and 55 MPa) at a stress rate of 30 MPa/s, and (c) for the cases with same stress level (15 ± 50 MPa) but at different rates (i.e., 6, 30, and 90 MPa/s).
Figure 5.39 Experimental and simulated stress–strain curves of the PEI for the load case with a mean stress of 32.5 MPa and stress amplitude of 32.5 MPa: (a) first hysteresis loops, (b) experimental stress–strain curves for 200 cycles, and (c) simulated stress–strain curves for 200 cycles.
Figure 5.40 Experimental and simulated curves of ratchetting strain versus the number of cycles for the PEI: (a) for the cases with same stress level (32.5 ± 32.5 MPa) but different peak‐hold times (i.e., 0, 5, and 20 s), (b) for the cases with same stress level (35 ± 35 MPa) but at various stress rates (i.e., 1, 6, and 30 MPa/s), and (c) for the cases at same stress rate (30 MPa/s) but with two stress levels (i.e., 32.5 ± 32.5 MPa and 35 ± 35 MPa).
Figure 5.41 Multilevel loading–unloading recovery (20 → 40 → 50 → 55 → 60 → 65 → 70 → 71 MPa): (a) first cycle, (b) second cycle, (c) third cycle, (d) fourth cycle, (e) fifth cycle, (f) sixth cycle, (g) seventh cycle and (h) eighth cycle.
Figure 5.42 Strain–time curves for the process of strain recovery at zero stress point with various peak stresses.
Figure 5.43 Strain–time curves for the creep recovery test.
Figure 5.44 Cyclic deformation with a mean stress of 25 MPa and stress amplitude of 25 MPa at a stress rate of 1.2 MPa/s: (a) experimental stress–strain curve, (b) simulated stress–strain curve, and (c) evolution curves of peak and valley strains.
Figure 5.45 Cyclic deformation with a mean stress of 33 MPa and stress amplitude of 26.4 MPa at a stress rate of 1.0 MPa/s: (a) experimental stress–strain curve, (b) simulated stress–strain curve, (c) evolution curves of peak and valley strains, and (d) strain–time curves for strain recovery at zero stress point after cyclic deformation.
Figure 5.46 Cyclic deformation with a mean stress of 26.4 MPa and stress amplitude of 33 MPa at a stress rate of 1.0 MPa/s: (a) experimental stress–strain curve, (b) simulated stress–strain curve, (c) evolution curves of peak and valley strains, and (d) strain–time curves for strain recovery at zero stress point after cyclic deformation.
Figure 5.47 Cyclic deformation with a mean stress of 19.8 MPa and stress amplitude of 39.6 MPa at a stress rate of 1.0 MPa/s: (a) experimental stress–strain curve, (b) simulated stress–strain curve, (c) evolution curves of peak and valley strains, and (d) strain–time curves for strain recovery at zero stress point after cyclic deformation.
Figure 5.48 Cyclic deformation with a mean stress of 13.2 MPa and stress amplitude of 46.2 MPa at a stress rate of 1.0 MPa/s: (a) experimental stress–strain curve, (b) simulated stress–strain curve, (c) evolution curves of peak and valley strains, and (d) strain–time curves for strain recovery at zero stress point after cyclic deformation.
Figure 5.49 Evolution curves of the elastic compliance during the cyclic deformation under tension–unloading and tension–compression conditions.
Figure 5.50 Evolution curves with the same mean stress (50 MPa) and stress amplitudes (10 MPa) but at various stress rates: (a) valley strains and (b) peak strains.
Figure 5.51 Cyclic deformation with three stress levels (40 ± 10 MPa → 50 ± 10 MPa → 40 ± 10 MPa) and at a stress rate of 1.2 MPa/s: (a) experimental stress–strain curve, (b) simulated stress–strain curve, and (c) evolution curves of peak and valley strains.
Figure 5.52 Cyclic deformation with three stress levels (40 ± 10 MPa → 40 ± 20 MPa → 40 ± 10 MPa) and at a stress rate of 1.2 MPa/s: (a) experimental stress–strain curve, (b) simulated stress–strain curve, and (c) evolution curves of peak and valley strains.
Chapter 06
Figure 6.1 Curves of axial stress versus strain for the matrix and composites at room temperature and 573 K: (a) at a constant strain rate; (b) at a varied strain rate.
Figure 6.2 Results of stress response for the matrix under the strain‐controlled cyclic loading and at room temperature: (a) stress–strain curves; (b) curves of responded stress amplitude versus number of cycles.
Figure 6.3 Curves of responded stress amplitude versus number cycles for the composites under the strain‐controlled cyclic loading and at room temperature.
Figure 6.4 Curves of responded stress amplitude versus number cycles for the composites under the strain‐controlled cyclic loading and at 573 K.
Figure 6.5 Ratchetting results of the unreinforced matrix in the cyclic test with varied mean stress: (a) stress–strain curves; (b) curves of ratchetting strain versus number of cycles.
Figure 6.6 Ratchetting results of the unreinforced matrix in the cyclic test with varied stress amplitude: (a) stress–strain curves; (b) curves of ratchetting strain versus number of cycles.
Figure 6.7 Ratchetting results of the composite with
V
f
= 14% in the cyclic test with varied mean stress: (a) stress–strain curves; (b) curves of ratchetting strain versus number of cycles.
Figure 6.8 Ratchetting results of the composite with
V
f
= 21% in the cyclic test with varied mean stress: (a) stress–strain curves; (b) curves of ratchetting strain versus number of cycles.
Figure 6.9 Ratchetting results of the composite with
V
f
= 14% in the cyclic test with varied stress amplitude: (a) stress–strain curves; (b) curves of ratchetting strain versus number of cycles.
Figure 6.10 Ratchetting results of the composite with
V
f
= 21% in the cyclic test with varied stress amplitude: (a) stress–strain curves; (b) curves of ratchetting strain versus number of cycles.
Figure 6.11 Rate‐ or time‐dependent ratchetting results of the composite with
V
f
= 21%: (a) stress–strain curves (at stress rate of 25 MPa/s); (b) curves of ratchetting strain versus number of cycles at two stress rates.
Figure 6.12 Rate‐ or time‐dependent ratchetting results of the composite with
V
f
= 21%: (a) stress–strain curves (peak stress hold for 15 s); (b) curves of ratchetting strain versus number of cycles.
Figure 6.13 Ratchetting results of the composite with
V
f
= 14% in the cyclic test with varied mean stress at 573 K: (a) stress–strain curves; (b) curves of ratchetting strain versus number of cycles.
Figure 6.14 Ratchetting results of the composite with
V
f
= 21% in the cyclic test with varied mean stress at 573 K: (a) stress–strain curves; (b) curves of ratchetting strain versus number of cycles.
Figure 6.15 Ratchetting results of the composite with
V
f
= 14% in the cyclic test with varied stress amplitude at 573 K: (a) stress–strain curves; (b) curves of ratchetting strain versus number of cycles.
Figure 6.16 Ratchetting results of the composite with
V
f
= 21% in the cyclic test with varied stress amplitude at 573 K: (a) stress–strain curves; (b) curves of ratchetting strain versus number of cycles.
Figure 6.17 Rate‐ or time‐dependent ratchetting results of the composite with
V
f
= 21% at 573 K: (a) stress–strain curves (at stress rate of 12.5 MPa/s); (b) curves of ratchetting strain versus number of cycles at two stress rates.
Figure 6.18 Rate‐ or time‐dependent ratchetting results of the composite with
V
f
= 14% at 573 K: (a) stress–strain curves (peak stress hold for 60 s); (b) curves of ratchetting strain versus number of cycles.
Figure 6.19 Representative volume elements and finite element meshes of the composites.
Figure 6.20 Experimental and simulated results of tensile stress–strain curves at a strain rate of 0.001/s,
μ
= 0.05: (a) the matrix; (b) the composites with
V
f
= 14% and 21%.
Figure 6.21 Experimental and simulated results of the matrix in the uniaxial strain‐controlled cyclic test with a strain amplitude of ±0.6% and at a strain rate of 0.001/s,
μ
= 0.05.
Figure 6.22 Experimental and simulated results of the composites in the uniaxial strain‐controlled cyclic test with a strain amplitude of ±0.6% and at a strain rate of 0.001/s,
μ
= 0.05: (a) with
V
f
= 14%; (b) with
V
f
= 21%.
Figure 6.23 Experimental and simulated uniaxial ratchetting of the matrix with a stress amplitude of ±280 MPa and mean stress of 25 MPa and at a stress rate of 25 MPa/s,
μ
= 0.05.
Figure 6.24 Experimental and simulated uniaxial ratchetting of the composites at a stress rate of 25 MPa/s,
μ
= 0.05: (a) with
V
f
= 14% and 25 ± 280 MPa; (b) with
V
f
= 21% and 55 ± 280 MPa.
Figure 6.25 Finite element model of the composites with an interfacial layer.
Figure 6.26 Simulated monotonic tensile stress–strain curves of the composite with
V
f
= 14% and different interfacial moduli
E
i
.
Figure 6.27 Simulated ratchetting of the composite with
V
f
= 14% and different interfacial moduli
E
i
.
Figure 6.28 Isograms of axial strain distribution in the matrix of the composite with
V
f
= 14% and a perfect interfacial bonding and at different monotonic tensile stages: (a)
ε
appl.
= 0.12%; (b)
ε
appl.
= 0.6%; (c)
ε
appl.
= 1.0%.
Figure 6.29 Isograms of axial strain distribution in the matrix and interfacial layer of the composite with
V
f
= 14%,
E
i
= 20 GPa and at different monotonic tensile stages: (a)
ε
appl.
= 0.12%; (b)
ε
appl.
= 0.6%; (c)
ε
appl.
= 1.0%.
Figure 6.30 Isograms of axial strain distribution in the matrix of the composite with
V
f
= 14% and a perfect interfacial bonding and at peak stress point (25 ± 280 MPa): (a) 1st cycle; (b) 10th cycle.
Figure 6.31 Isograms of axial strain distribution in the matrix and interfacial layer of the composite with
V
f
= 14%,
E
i
= 20 GPa and at peak stress point (25 ± 280 MPa): (a) 1st cycle; (b) 10th cycle.
Figure 6.32 Simulated results of the composite with
V
f
= 14% and different interfacial yielding strengths
σ
yi
(
E
i
= 20 GPa and
H
i
= 4 GPa): (a) monotonic tensile stress–strain curves; (b) uniaxial ratchetting with 25 ± 280 MPa (10c).
Figure 6.33 Simulated results of the composite with
V
f
= 14% and different interfacial tangent moduli
H
i
(
E
i
= 20 GPa and
σ
yi
= 150 MPa): (a) monotonic tensile stress–strain curves; (b) uniaxial ratchetting with 25 ± 280 MPa (10c).
Figure 6.34 3D multiparticle cubic unit cell (a) and its finite element mesh (b).
Figure 6.35 Simulated results of the composite with
V
f
= 14% and by different unit cells: (a) monotonic tensile stress–strain curves; (b) uniaxial ratchetting with 25 ± 280 MPa (10c).
Figure 6.36 Isograms of axial strain distribution in the matrix of the composite with
V
f
= 14% and at different stages of monotonic tension: (a)
ε
appl.
= 0.12%; (b)
ε
appl.
= 0.6%; (c)
ε
appl.
= 1.0%.
Figure 6.37 Isograms of axial strain distribution in the matrix of the composite with
V
f
= 14% and at peak stress points of ratchetting tests (25 ± 280 MPa): (a) 1st cycle; (b) 10th cycle.
Figure 6.38 Experimental and simulated ratchetting of the composites with (a)
V
p
= 14% and (b)
V
p
= 21% (
E
i
= 20 GPa,
σ
yi
= 150 MPa, and
H
i
= 4 GPa).
Figure 6.39 Experimental and simulated results of tensile stress–strain curves for the composites at room temperature and
μ
= 0.05: (a) at a constant strain rate of 0.001/s; (b) at varied strain rate.
Figure 6.40 Experimental and simulated results of tensile stress–strain curves for the composites at 573 K and varied strain rate,
μ
= 0.04.
Figure 6.41 Experimental and simulated results of cyclic stress–strain curves for the composite with
V
f
= 14% in the uniaxial strain‐controlled cyclic test with a strain amplitude of ±0.6% and peak strain hold for 10 s, at room temperature and strain rate of 0.002/s,
μ
= 0.05.
Figure 6.42 Experimental and simulated results of uniaxial time‐dependent ratcheting for the composites obtained at different stress rates (
V
f
= 21%, at room temperature, 50 ± 280 MPa,
μ
= 0.05): (a) cyclic stress–strain curves; (b) results of ratchetting strain versus number of cycles.
Figure 6.43 Experimental and simulated results of uniaxial time‐dependent ratchetting for the composites obtained with different hold times at peak stress points (
V
f
= 21%, at room temperature and a stress rate of 25 MPa/s, 50 ± 280 MPa,
μ
= 0.05): (a) cyclic stress–strain curves; (b) results of ratchetting strain versus number of cycles.
Figure 6.44 Experimental and simulated uniaxial time‐dependent ratchetting of the composites: (a) obtained at different stress rates (
V
f
= 21%, at 573 K, 45 ± 215 MPa,
μ
= 0.04, without any hold); (b) obtained with different hold times at peak stress points (
V
f
= 14%, at 573 K and a stress rate of 3.5 MPa/s, 90 ± 140 MPa,
μ
= 0.04).
Figure 6.45 Experimental and simulated tensile stress–strain curves of 6061‐T6Al alloy matrix: (a) with various
k
; (b) with various
μ
0
; (c) with different tangent operators; (d) with various Δ
ε
.
Figure 6.46 Experimental and predicted tensile stress–strain curves of the composites.
Figure 6.47 Experimental and predicted cyclic stress–strain hysteresis loops in the uniaxial strain‐controlled cyclic tests: (a) for the matrix; (b) for the composite with
v
1
= 14%; (c) for the composite with
v
1
= 21%.
Figure 6.48 Simulated uniaxial ratchetting of the matrix (1st cycle): (a) with different tangent operators and Δ
σ
= 3.05 MPa; (b) with various Δ
σ
.
Figure 6.49 Experimental and simulated ratchetting of the matrix: (a) with various
μ
0
and
k
= 21.2; (b) with various
k
.
Figure 6.50 Experimental and predicted ratchetting of the composite with
v
1
= 14% (25 ± 280 MPa, 50 cycles): (a) by the
C
ep
; (b) by the
C
alg
with various Δ
σ
.
Figure 6.51 Experimental and predicted ratchetting of the composite with
v
1
= 14% (15 ± 280 MPa, 50 cycles): (a) by the
C
ep
; (b) by the
C
alg
with various Δ
σ
.
Figure 6.52 Experimental and predicted ratchetting of the composite with
v
1
= 21%: (a) 55 ± 280 MPa, 50 cycles; (b) 85 ± 280 MPa, 50 cycles.
Figure 6.53 Experimental and simulated tensile stress–strain curves at room temperature: (a) the matrix at two strain rates of 1 × 10
−3
and 5 × 10
−3
s
−1
; (b) the composites at varied strain rate.
Figure 6.54 Cyclic stress–strain hysteresis loops under the strain‐controlled cyclic loading conditions at a strain rate of 2 × 10
−3
s
−1
and at room temperature: (a) the matrix; (b) the composite with
v
1
= 14%; (c) the composite with
v
1
= 21%; (d) the composite with
v
1
= 14% and peak strain hold for 10 s.
Figure 6.55 Experimental and simulated ratchetting of the composites (
v
1
= 21%, 50 ± 280 MPa) at room temperature: (a) at two stress rates; (b) with different hold times at peak stress points.
Figure 6.56 Experimental and simulated tensile stress–strain curves at varied strain rate and at 573 K: (a) the matrix; (b) the composites.
Figure 6.57 Experimental and predicted uniaxial time‐dependent ratchetting at 573 K: (a) the composite with
v
1
= 14% and in load case of 90 ± 140 MPa with different hold times at peak stress point; (b) the composite with
v
1
= 21% and in load case of 45 ± 215 MPa at two stress rates.
Chapter 07
Figure 7.1 Cyclic stress–strain curves of a super‐elastic NiTi SMA with various applied peak strains: (a) 5%; (b) 6%; (c) 8%; (d) 10%.
Figure 7.2 Stress–strain curves of super‐elastic NiTi SMA in the cyclic tension–unloading with various peak stresses: (a) 450 MPa; (b) 500 MPa; (c) 550 MPa; (d) 600 MPa.
Figure 7.3 Results of super‐elastic NiTi SMA obtained in the cyclic tension–unloading with various peak stresses: (a) curves of nominal elastic modulus versus the number of cycles (with peak stresses of 450 and 500 MPa); (b) curves of peak strain, residual strain, and ratchetting strain versus the number of cycles; (c) curves of nominal transformation stress
versus the number of cycles; (d) curves of dissipation energy
W
d
versus the number of cycles; (e) curves of nominal transformation stress
versus the number of cycles.
Figure 7.4 Stress–strain curves of super‐elastic NiTi SMA in the cyclic tension–tension with a constant stress amplitude of 125 MPa and two mean stresses: (a) 325 MPa; (b) 425 MPa.
