Stress and Strain Measures for Orthotropic Metals at Large Nonproportional Plastic Strain Histories

2009 ◽  
pp. 203-222
Author(s):  
Milan V. Mićunović
Keyword(s):  
Plastic Strain ◽  
Stress And Strain ◽  
Strain Measures

A Critical Review of Existing Hydrogen Diffusion Models Accounting for Different Physical Variables

2014 ◽  
Vol 225 ◽  
pp. 13-18 ◽  
Author(s):  
Jesús Toribio ◽  
Viktor Kharin
Keyword(s):  
Plastic Strain ◽  
Continuum Mechanics ◽  
Critical Review ◽  
Hydrogen Diffusion ◽  
Hydrostatic Stress ◽  
Stress And Strain ◽  
Material Microstructure ◽  
Continuum Modelling ◽  
Physical Variables ◽  
Cumulative Plastic Strain

The present paper offers a continuum modelling of trap-affected hydrogen diffusion in metals and alloys, accounting for different physical variables of both macroscopic nature (i.e., related to continuum mechanics, e.g., stress and strain) and microscopic characteristics (material microstructure, traps, etc.). To this end, the model of hydrogen diffusion assisted by the gradients of both hydrostatic stress and cumulative plastic strain,stress-and-strain assisted hydrogen diffusion, proposed and frequently used by the authors of the present paper (Toribio & Kharin) is analysed in addition to other well-known models such as those proposed by (i) McNabb & Foster, (ii) Oriani, (iii) Leblond & Dubois, (iv) Sofronis & McMeeking, (v) Krom and Bakker, showing their physical and mathematical differences and similarities to account for different physical variables.

Constitutive inequalities for isotropic elastic solids under finite strain

1970 ◽  
Vol 314 (1519) ◽  
pp. 457-472 ◽  
Keyword(s):  
Scalar Product ◽  
Finite Strain ◽  
Strain Analysis ◽  
Stress And Strain ◽  
Elastic Solids ◽  
Intrinsic Interest ◽  
Typical Member ◽  
Rates Of Change ◽  
Constitutive Inequalities ◽  
Strain Measures

Possible restrictions on isotropic constitutive laws for finitely deformed elastic solids are examined from the standpoint of Hill (1968). This introduced the notion of conjugate pairs of stress and strain measures, whereby families of contending inequalities can be generated. A typical member inequality stipulates that the scalar product of the rates of change of certain conjugate variables is positive in all circumstances. Interrelations between the various inequalities are explored, and some statical implications are established. The discussion depends on several ancillary theorems which are apparently new; these have, in addition, an intrinsic interest in the broad field of basic stress—strain analysis.

Effect of process parameters on stress and strain of hybrid deposition and micro-rolling

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Xushan Zhao ◽  
Yuanxun Wang ◽  
Guilan Wang ◽  
Runsheng Li ◽  
Haiou Zhang
Keyword(s):  
Residual Stress ◽  
Plastic Strain ◽  
Three Dimensional ◽  
Substantial Effect ◽  
Weld Bead ◽  
Stress And Strain ◽  
Residual Tensile Stress ◽  
Content Type ◽  
Orthogonal Optimization ◽  
Selection Of

Purpose This paper aims to summarize the influence law of hybrid deposited and micro-rolling (HDMR) technology on the shaping strain and residual stress. And the rolling parameters combination was further optimized to guide the actual production. Design/methodology/approach This paper proposed a three-dimensional coupled thermo-mechanical model of the HDMR process. The validated model is used to investigate the influences of rolling parameters on stress and plastic strain (the distance between the energy source and roller [De–r], the rolling compression [cr] and the friction coefficient [fr]). The orthogonal optimization of three factors and three levels was carried out. The influence of rolling parameters on the plastic strain and residual stress is analyzed. Findings The simulation results show that HDMR technology can effectively increase the shaping strain of the weld bead and reduce the residual tensile stress on the weld bead surface. Furthermore, the influence of rolling parameters on stress and strain is obtained by orthogonal analysis, and the corresponding optimal combination is proposed. Also, the rolling temperature significantly affects the residual stress, and the rolling reduction has a substantial effect on the plastic deformation. Research limitations/implications Owing to the choice of research methods, this paper failed to study microstructure evolution. Originality/value This paper provides a reference principle for the optimal selection of rolling parameters in HDMR.

Compact Basis Free Relations for Stress Tensors Conjugate to Hill’s Strain Measures

2006 ◽  
Author(s):  
Reza Naghdabadi ◽  
Mohsen Asghari ◽  
Kamyar Ghavam
Keyword(s):  
Strain Tensor ◽  
Three Dimensional ◽  
Inner Product ◽  
Stress And Strain ◽  
Conjugate Pair ◽  
Stress Tensors ◽  
Plastic Materials ◽  
The Right ◽  
Elastic Plastic Materials ◽  
Strain Measures

If the double contraction of a stress tensor such as T and rate of a Lagrangean strain tensor such as E, i.e. T : E˙, produces the stress power then these stress and strain tensors are called a conjugate pair. The applications of the conjugate stress and strain measures are in the development of the basic relations in nonlinear continuum mechanics analysis such as modeling of constitutive equations of elastic-plastic materials. In this paper relations for stress tensors conjugate to an arbitrary Lagrangean strain measure of Hill’s class are obtained. The results of this paper are more compact and simpler in compare with those available in the literature. The results are valid for the three dimensional Euclidean inner product space and the case of distinct eigenvalues of the right stretch tensor U.

scholarly journals Description of Residual Stress and Strain Fields in FGM Hollow Disc Subject to External Pressure

Materials ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 440 ◽  
Author(s):  
Stanislav Strashnov ◽  
Sergei Alexandrov ◽  
Lihui Lang
Keyword(s):  
Elastic Modulus ◽  
Plastic Strain ◽  
Yield Stress ◽  
Plastic Region ◽  
External Pressure ◽  
Plastic Strain Rate ◽  
Constant Thickness ◽  
Stress And Strain ◽  
Strain Fields ◽  
Tensile Yield Stress

Elastic/plastic stress and strain fields are obtained in a functionally graded annular disc of constant thickness subject to external pressure, followed by unloading. The elastic modulus and tensile yield stress of the disc are assumed to vary along the radius whereas the Poisson’s ratio is kept constant. The flow theory of plasticity is employed. However, it is shown that the equations of the associated flow rule, which are originally written in terms of plastic strain rate, can be integrated with respect to the time giving the corresponding equations in terms of plastic strain. This feature of the solution significantly facilitates the solution. The general solution is given for arbitrary variations of the elastic modulus and tensile yield stress along the radial coordinate. However, it is assumed that plastic yielding is initiated at the inner radius of the disc and that no other plastic region appears in the course of deformation. The solution in the plastic region at loading reduces to two ordinary differential equations. These equations are solved one by one. Unloading is assumed to be purely elastic. This assumption should be verified a posteriori. An illustrative example demonstrates the effect of the variation of the elastic modulus and tensile yield stress along the radius on the distribution of stresses and strains at the end of loading and after unloading. In this case, it is assumed that the material properties vary according to power-law functions.

Unified Basis-Free Relation Between Two Stress Tensors Conjugate to Arbitrary Hill’s Strain Measures

2006 ◽  
Author(s):  
Mohsen Asghari ◽  
Reza Naghdabadi
Keyword(s):  
Arbitrary Dimension ◽  
Rate Of Change ◽  
The Body ◽  
Inner Product ◽  
Adiabatic Process ◽  
Stress And Strain ◽  
Stress Tensors ◽  
Two Measures ◽  
The Right ◽  
Strain Measures

The concept of energy conjugacy for stress and strain measures states that a stress tensor T is conjugate to a strain measure E if T: E˙ provides the rate of change of the internal energy per unit reference volume of the body in an adiabatic process. The applications of the conjugate stress and strain measures are in the development of the basic relations in nonlinear analysis of solids. In this paper using eigenprojection method, unified explicit basis-free relation between two arbitrary stress tensors T(f) and T(g), respectively conjugate to two measures of Hill’s strains is determined. The result is valid for arbitrary dimension of the Euclidean inner product space and for all cases of distinct and repeated eigenvalues of the right stretch tensor U.

The relation between stress and strain in the initial stage of plastic strain under two-axial tension

1967 ◽  
Vol 3 (12) ◽  
pp. 80-81 ◽  
Author(s):  
I. A. Kozlov ◽  
A. A. Lebedev ◽  
V. L. Akhremenko
Keyword(s):  
Plastic Strain ◽  
Stress And Strain ◽  
Axial Tension ◽  
Initial Stage

scholarly journals Why titanium alloys withstand more strain under dwell-fatigue than under fatigue?

2020 ◽  
Vol 321 ◽  
pp. 11080
Author(s):  
S. Hémery ◽  
A. Naït-Ali ◽  
C. Lavogiez ◽  
P. Villechaise
Keyword(s):  
Crack Initiation ◽  
Plastic Strain ◽  
Room Temperature ◽  
Maximum Stress ◽  
Fourier Transforms ◽  
Stress And Strain ◽  
Cyclic Testing ◽  
Applied Loading ◽  
Dwell Fatigue ◽  
Number Of Cycles

Experimental observations reveal that crack initiation proceeds at a reduced number of cycles if a load hold at maximum stress is introduced during cyclic testing. Although this feature was extensively investigated and stems from the occurrence of room temperature creep, other differences between fatigue and dwell-fatigue behaviors are still to be clarified. In particular, a higher plastic strain is cumulated prior to failure if the load hold is present. This observation highlights differences in the deformation behavior depending on the applied loading. The present article reports an investigation of this point using Fast-Fourier transforms based crystal plasticity simulations of the stress and strain field. Significant differences were evidenced and discussed in light of experimental results reported in the literature. In particular, the occurrence of crack initiation for different cumulated plastic strain depending on the loading conditions is elucidated.

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