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Stress relaxation

About: Stress relaxation is a research topic. Over the lifetime, 12959 publications have been published within this topic receiving 270815 citations.


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TL;DR: In this article, a non-linear differential equation for uniaxial viscoplasticity is transformed into an equivalent integral equation, which employs total strain only and is symmetric with respect to the origin and applies for tension and compression.
Abstract: A previously proposed first order non-linear differential equation for uniaxial viscoplasticity, which is non-linear in stress and strain but linear in stress and strain rates, is transformed into an equivalent integral equation. The proposed equation employs total strain only and is symmetric with respect to the origin and applies for tension and compression. The limiting behavior for large strains and large times for monotonic, creep and relaxation loading is investigated and appropriate limits are obtained. When the equation is specialized to an overstress model it is qualitatively shown to reproduce key features of viscoplastic behavior. These include: initial linear elastic or linear viscoelastic response: immediate elastic slope for a large instantaneous change in strain rate normal strain rate sensitivity and non-linear spacing of the stress-strain curves obtained at various strain rates; and primary and secondary creep and relaxation such that the creep (relaxation) curves do not cross. Isochronous creep curves are also considered. Other specializations yield wavy stress-strain curves and inverse strain rate sensitivity. For cyclic loading the model must be modified to account for history dependence in the sense of plasticity.

78 citations

Journal ArticleDOI
TL;DR: In this article, a relaxation framework for the theory of thermoelastic nonconductors of heat, equipped with globally defined entropy functions for the associated relaxation process, is presented.
Abstract: .The theory of materials with internal state variables of Coleman & Gurtin [CG] provides a natural framework to investigate the structure of relaxation approximations of conservation laws from the viewpoint of continuum thermomechanics. After reviewing the requirements imposed on constitutive theories by the principle of consistency with the Clausius‐Duhem inequality, we pursue two specific theories pertaining to stress relaxation and relaxation of internal energy. They each lead to a relaxation framework for the theory of thermoelastic non‐conductors of heat, equipped with globally defined “entropy” functions for the associated relaxation process. Next, we consider a semilinear model problem of stress relaxation. We discuss uniform stability and compactness for solutions of the relaxation system in the zero‐relaxation limit, and establish convergence to the system of isothermal elastodynamics by using compensated compactness. Finally, we prove a strong dissipation estimate for the relaxation approximations proposed in Jin & Xin [JX] when the limit system is equipped with a strictly convex entropy.

78 citations

Journal ArticleDOI
TL;DR: In this paper, a single mechanism of interfacial viscous shearing between the two eutectic phases is proposed for both creep and stress relaxation on the RSA II instrument modified to use a 0.5 mm diameter cylindrical punch under 1.5-47 MPa punching stress and within a temperature range of 25 °C to 110 °C.
Abstract: Impression creep and stress relaxation experiments on the SnPb eutectic alloy were carried out in the RSA II instrument modified to use a 0.5 mm diameter cylindrical punch under 1.5–47 MPa punching stress and within a temperature range of 25 °C to 110 °C. Based on a power law between the impression velocity and stress or between the stress rate and stress, the exponent increased with stress from 1 to 3.5 within the temperature range 80–110 °C and 2.5 to 6 within the range 25–65 °C. These exponents were generally comparable to those reported in the literature. Because of the change of stress exponent, several mechanisms have been proposed. However, the stress dependence was found to obey a hyperbolic sine function of stress for all the stresses and temperatures studied. Similarly before using the hyperbolic sine function, the activation energy was found to increase with stress, an abnormal behaviour. Fortunately, after using the hyperbolic sine function, a single activation energy, 55 kJ mol−1 was obtained. Based on the present data, a single mechanism of interfacial viscous shearing between the two eutectic phases is proposed for both creep and stress relaxation. In addition to the effect of stress and temperature, the impression velocity based on this model should be directly proportional to the punch radius and inversely proportional to the nth (n = 1–3) power of the size of phase particles. These predictions are consistent with available information in the literature.

78 citations

Journal ArticleDOI
TL;DR: Based on a stress invariant hypothesis and a stress/strain relaxation procedure, an analytical approach is forwarded for approximate determination of residual stresses and strain accumulation in elastic-plastic stress analysis of rolling contact as discussed by the authors.
Abstract: Based on a stress invariant hypothesis and a stress/strain relaxation procedure, an analytical approach is forwarded for approximate determination of residual stresses and strain accumulation in elastic-plastic stress analysis of rolling contact. For line rolling contact problems, the proposed method produces residual stress distributions in favorable agreement with the existing finite element findings. It constitutes a significant improvement over the Merwin-Johnson and the McDowell-Moyar methods established earlier. The proposed approach is employed to study combined rolling and sliding for selected materials, with special attention devoted to 1070 steel behavior. Normal load determines the subsurface residual stresses and the size of the subsurface plastic zone. On the other hand, the influence of tangential force penetrates to a depth of 0.3a, where a is the half width of the contact area, and has diminishing influence on the residual stresses beyond this thin layer. A two-surface plasticity model, commensurate with nonlinear kinematic hardening, is utilized in solution of incremental surface displacements with repeated rolling. It is demonstrated that a driven wheel undergoes greater plastic deformation than the driving wheel, suggesting that the driven wheel experiences enhanced fatigue damage. Furthermore, the calculated residual stresses are compared with the existing experimental data from the literature with exceptional agreements.

77 citations

Journal ArticleDOI
Shi-Qing Wang1, Yangyang Wang1, Shiwang Cheng1, Xin Li1, Xiangyang Zhu1, Hao Sun1 
TL;DR: In this paper, the authors discuss four types of new experiments that can improve the current theoretical description of nonlinear rheology of entangled polymers and show that a slowly imposed strain can result in nonmonotonic evolution of the state of chain entanglement during quiescent relaxation.
Abstract: The present work discusses four types of new experiments that can improve the current theoretical description of nonlinear rheology of entangled polymers. First, a slowly imposed strain is found to result in nonmonotonic evolution of the state of chain entanglement during quiescent relaxation, consistent with the idea of chain disentanglement after step shear. Second, the stress relaxation upon a sizable step strain is found to be identical to that for small step strain, consistent with a molecular scenario that a strained entangled melt has an entropic barrier to resist chain retraction. Third, the ability of a step-strained polymer to undergo elastic recovery is found to be the same up to strain amplitude of unity, and a sample sheared for a period much longer than the Rouse time is shown to still undergo nearly full elastic recovery. Fourth, an entangled melt, stretched at a rate significantly lower than the Rouse relaxation rate, undergoes full elastic recovery until the point of tensile force maximum...

77 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023145
2022390
2021266
2020276
2019270
2018281