Cyclic Plasticity of Engineering Materials: Experiments and Models

By Guozheng Kang and Qianhua Kan

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.

• Language: English
• Publisher: Wiley
• Release date: Mar 10, 2017
• ISBN: 9781119180814

Book preview

Introduction

Cyclic plasticity concerns the rate‐independent or rate‐dependent elastoplastic stress–strain responses of engineering materials presented under the cyclic loading conditions, including experimental observations and the construction of constitutive models. It plays a very important role in the fatigue analysis and reliability assessment of engineering structures and then should be realized experimentally and theoretically in advance. However, the cyclic plasticity is very complicated, since so many factors may influence the cyclic plastic stress–strain responses of the materials under different cyclic loading conditions, such as uniaxial and multiaxial loading paths, loading rate or loading frequency, ambient temperature and loading mode, and so on. Before the discussion of cyclic plasticity, it is necessary to introduce some basic knowledge points of the monotonic elastoplastic deformation of engineering materials. Therefore, in this chapter, some fundamental experimental phenomena of monotonic and cyclic plasticity are introduced briefly, which is very helpful for the readers to understand the cyclic plasticity and corresponding constitutive models. More recent advances in the cyclic plasticity of engineering materials, including some advanced materials such as high‐performance polymers, particle‐reinforced metal matrix composites, and shape memory alloy (SMA), will be addressed in the next chapters.

I.1 Monotonic Elastoplastic Deformation

Plasticity is a key issue of material deformation and is generally faced by the metallic structure components subjected to high applied loads, such as those caused by earthquake, dynamic impact, and high stress concentration. The distinctive phenomenon of plasticity is its irreversibility after the unloading due to the resulted damage in the material by the plastic deformation. For ductile metals (whose stretch ratio is larger than 5%, as classified in the textbook of Mechanics of Materials), their plasticity can be investigated firstly and simply by monotonic tensile tests. Three representative tensile stress–strain curves obtained in the monotonic tensile tests of ductile metals are given in Figure I.1, where Figure I.1a shows the stress–strain curve of low carbon steel, Figure I.1b gives that of stainless steel, and Figure I.1c illustrates that of tempered low alloy high strength steel.

Figure I.1 Monotonic tensile stress–strain curves of ductile metals. (a) Low carbon steel (b) stainless steel, and (c) tempered low alloy high strength steel.

It is concluded that at the first stage of monotonic tension, ductile metals deform linearly, and the axial stress is in a linear relationship with the axial strain. During unloading, the resulted strain can be totally recovered, and such a recoverable strain is named as elastic strain. However, during the further monotonic tension, an apparent nonlinear deformation occurs after a critical stress is reached, and certain irrecoverable strain is observed after the unloading hereafter. The irrecoverable strain is denoted as plastic strain, and the critical stress is called as yielding stress. For low carbon steel, as shown in Figure I.1a, an apparent yielding plateau (where the strain increases progressively without an obvious increase in the stress) occurs, and the strain hardening (i.e., the stress increases further with the increase of strain) develops till the ultimate strength of the steel is reached. For stainless steel, no apparent yielding plateau is observed, and a nominal yielding stress, such as σp0.2 (whose definition can be referred to any textbook of Mechanics of Materials), is prescribed to judge whether the plastic yielding occurs or not. For tempered low alloy high strength steel, the yielding stress is much higher than that of low carbon steel and stainless steel, but its strain hardening is not as remarkable as that of the former two steels.

I.2 Cyclic Elastoplastic Deformation

Since the engineering structure components are often subjected to a kind of cyclic loading, especially for the components enduring the fatigue load, it is extremely necessary to investigate the cyclic stress–strain response of ductile metals. Although the loads acted on the structure components are not strictly prescribed as the strain‐ or stress‐controlled modes, these two distinctive modes are often used to experimentally investigate the cyclic elastoplastic deformation of ductile metals. Different cyclic stress–strain responses are observed under different controlled modes, even for the same metal.

I.2.1 Cyclic Softening/Hardening Features

Under the symmetrical uniaxial strain‐controlled cyclic loading conditions simply shown in Figure I.2 (where, a triangle load‐wave is used to keep the loading rate being the same per cycle), the peak and valley strains do not change with the increasing number of cycles since they are prescribed as the controlling factors, while the responding peak and valley stresses may vary during the cyclic loading, as shown in Figures I.3, I.4, and I.5, and such variations depend greatly on the different materials.

Figure I.2 Diagram of triangle load‐wave for single‐step strain‐controlled cyclic loading.

Figure I.3 Cyclic stress–strain curves of cyclic hardening materials (a) and the variation of responding stress amplitude with the number of cycles (b).

Figure I.4 Cyclic stress–strain curves of cyclic softening materials (a) and the variation of responding stress amplitude with the number of cycles (b).

Figure I.5 Cyclic stress–strain curves of cyclic stabilizing materials (a) and the variation of responding stress amplitude with the number of cycles (b).

Referring to the variations of responding stress amplitudes (i.e., half of the difference between responding peak and valley stresses measured in the tests and defined by Equation (I.1)), the engineering materials can be classified as three groups, that is,

(I.1)

where the σmax and σmin are the maximum and minimum responding stresses obtained per cycle.

Cyclic hardening materials. The responding stress amplitudes of the materials increase with the increasing number of cycles, as shown in Figure I.3. The representatives of cyclic hardening materials are stainless steels including 304 (Kang et al., 2002a), 304L (Taleb and Hauet, 2009), 316FR (Kobayashi et al., 2000), and 316L (Kang et al., 2001) stainless steels, and copper (Kang et al., 2011).

Cyclic softening materials. The responding stress amplitudes of the materials decrease with the increasing number of cycles, as shown in Figure I.4. The representatives of cyclic softening materials are low alloy high strength steels, such as tempered 42CrMo (Kang and Liu, 2008) and 25CDV4.11 (Kang et al., 2005) steels.

Cyclic stabilizing materials. The responding stress amplitudes of the materials do not change apparently during the cyclic loading, as shown in Figure I.5. The representatives of cyclic stabilizing materials are annealed 42CrMo (Kang and Liu, 2008) steel and U71Mn rail steels (Kang et al., 2002b).

Further researches (e.g., Hassan et al., 1998; Kang et al., 2002a) have demonstrated that the multiaxial loading does not change the cyclic softening/hardening features, but it can cause additional hardening due to its nonproportionality, which will be discussed in details in Chapter 2. Moreover, it should be noted that the cyclic softening/hardening features of the materials can also occur during the stress‐controlled cyclic loading, where they are reflected by the increase/decrease of plastic strain and the widened/narrowed hysteresis loop, respectively.

I.2.2 Mean Stress Relaxation

Under the asymmetrical strain‐controlled cyclic loading conditions (i.e., the applied mean strain εm is not zero), the responding mean stress may decrease with the increasing number of cycles, as shown in Figure I.6, and such phenomenon is named as mean stress relaxation. The mean stress relaxation is a key problem encountered by the fastened components and should be realized clearly. The extent of mean stress relaxation is dependent on the applied strain level and different materials, which will be discussed in details in the next chapters.

Figure I.6 Mean stress relaxation occurred in asymmetrical strain‐controlled cyclic test. (a) Cyclic stress–strain curves and (b) curve of mean stress versus number of cycles.

I.2.3 Ratchetting

Under the stress‐controlled cyclic loading conditions, the peak and valley stresses do not change with the increasing number of cycles since they are prescribed as the controlling factors, while the responding peak and valley strains may vary during the cyclic loading, especially for the cases with nonzero mean stresses. During the stress‐controlled cyclic loading with nonzero mean stress, a cyclically accumulation of inelastic deformation will occur in the materials mainly in the direction of mean stress if the applied stress level is high enough (e.g., higher than the yield strength of the materials), which is called as ratchetting. The ratchetting and its dependence on the applied stress level can be shown in Figure I.7.

Figure I.7 Ratchetting occurred in the asymmetrical strain‐controlled cyclic tests and its dependence on the stress levels. (a) Elastic shakedown, (b) plastic shakedown, and (c) continuous ratchetting.

It is seen that (i) when the applied stress is small, an elastic shakedown of ratchetting will occur after certain cycles; (ii) when the applied stress is relatively high, a plastic shakedown of ratchetting will take place; and (iii) when the applied stress is high enough, a continuous ratchetting keeps going till the material fails.

As reviewed by Ohno (1990, 1997) and Kang (2008), the ratchetting varies with different materials and also depends on many external loading factors because it is a secondary deformation accumulated progressively cycle by cycle and superposed on the primary cyclic deformation. The main features of ratchetting can be outlined as follows for the ordinary metal materials, and the details can be referred to Chapter 2:

Ratchetting strain, defined as the increment of peak strain after each cycle by Chaboche et al. (1979) or the mean strain of each cycle by Kang et al. (2002a), progressively increases cycle by cycle, and its evolution rate increases with the increasing applied mean stress and stress amplitude.

Uniaxial ratchetting is caused by the difference between tensile and compression stress–strain curves in each cycle, that is, by an unclosed hysteresis loop, and the difference is related to anisotropic strain hardening (Ohno and Wang, 1993b). However, multiaxial ratchetting is a result of plastic flow that occurred under a nonproportionally multiaxial stress‐controlled cyclic loading, and the flow is affected significantly by the anisotropic strain hardening (Jiang and Sehitoglu, 1994). The multiaxial ratchetting varies with different multiaxial loading paths, and the multiaxial ratchetting of stainless steels is apparently weaker than the uniaxial one due to the additional hardening caused by the nonproportionally multiaxial loading paths (Jiang and Sehitoglu, 1994; McDowell, 1995; Yoshida, 1995; Bari and Hassan, 2000; Kang et al.,