Constraints on Moving Strong Discontinuity Surfaces in Dynamic Plane-Stress or Plane-Strain Deformations of Stable Elastic-Ideally Plastic Materials

1990 ◽  
Vol 57 (3) ◽  
pp. 569-576 ◽  
Author(s):  
Yinong Shen ◽  
W. J. Drugan
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Yield Condition ◽  
Strong Discontinuity ◽  
Dynamic Crack Propagation ◽  
Small Displacement ◽  
Flow Rule ◽  
Dynamic Crack ◽  
Plastic Materials ◽  
Discontinuity Surfaces

For dynamic deformations of compressible elastic-ideally plastic materials in the practically important cases of plane stress and plane strain, we investigate the possible existence of propagating surfaces of strong discontinuity (across which components of stress, strain, or material velocity jump) within a small-displacement-gradient formulation. For each case, an explicit proof of the impossibility of such a propagating surface (except at an elastic wave speed) is achieved for isotropic materials satisfying a Huber-Mises yield condition and associated flow rule, and we show that our method of proof can be generalized to a large class of anisotropic materials. Nevertheless, we demonstrate that moving surfaces of strong discontinuity cannot be ruled out for all stable (i.e., satisfying the maximum plastic work inequality) materials, as in the case of a material whose yield surface contains a linear portion. A clear knowledge of the conditions under which dynamically propagating strong discontinuity surfaces can and cannot exist is crucial to the attainment of correct and complete solutions to such practical elastic-plastic problems as dynamic crack propagation, impact and rapidly moving load problems, high-speed forming, cutting, and other manufacturing processes.

scholarly journals The influence of pavement degradation caused by cyclic loading on its failure mechanisms

2016 ◽  
Vol 11 (3) ◽  
pp. 179-187 ◽  
Author(s):  
Marcin Gajewski ◽  
Stanisław Jemioło
Keyword(s):  
Yield Condition ◽  
Limit Load ◽  
Flow Rule ◽  
Smooth Approximation ◽  
Simple Method ◽  
Plastic Properties ◽  
The Road ◽  
Plastic Materials ◽  
Number Of Cycles ◽  
Elastic Plastic Materials

In this paper, a simple method is proposed to estimate capacity of multilayered road structure including the degradation of the elastic and plastic properties of the constituent materials. In the study boundary value problem modeling interaction of wheels with road surface layer in the frame of large deformation theory for elastic-plastic materials was formulated. Plastic properties of the material were described by the flow rule un-associated with yield condition. The Coulomb-Mohr yield condition was assumed and the potential for plasticity is its smooth approximation. In addition, in constitutive modeling the dependence of the Young’s modulus and cohesion of the material from the number of cycles is taken into account. This paper presents qualitative findings in relation to mechanical behavior of the road structure, i.e., for example, the development of plastic zones with increasing load for un-degraded and degraded materials. In addition, a parametric study of the influence of the degradation ratio of the elasticity and plasticity properties for road structure failure mechanism (limit load value) was made.

An Analysis of the Plane-Strain Compression of Viscoplastic Materials

1997 ◽  
Vol 64 (2) ◽  
pp. 420-424 ◽  
Author(s):  
M. J. Adams ◽  
B. J. Briscoe ◽  
G. M. Corfield ◽  
C. J. Lawrence ◽  
T. D. Papathanasiou
Keyword(s):  
Plane Strain ◽  
Fluid Flows ◽  
Velocity Fields ◽  
Plane Strain Compression ◽  
Flow Rule ◽  
Strain Fields ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Calculated Stress ◽  
Associated Flow Rule

A theoretical analysis for the plane-strain compression of viscoplastic materials with a Tresca wall boundary condition is described. The analysis is based upon the incorporation of a viscoplastic associated flow rule into the cycloidal solution originally developed for rigid-perfectly plastic materials. The evolution of the calculated stress field suggests that the influence of strain rate hardening is similar to that reported previously for strain hardening. The calculated strain fields are elliptical in form and are consistent with those measured for a viscoplastic paste. Previous analyses of the compression of viscoplastic materials have employed the lubrication approximation for fluid flows with a resulting kinematic inconsistency in the predicted velocity fields.

Experimental Solution of Elastic-Plastic Plane-Stress Problems

1962 ◽  
Vol 29 (4) ◽  
pp. 735-743 ◽  
Author(s):  
P. S. Theocaris
Keyword(s):  
Plane Stress ◽  
Yield Condition ◽  
Strain Curve ◽  
Loading Path ◽  
Flow Rule ◽  
Stress And Strain ◽  
Stress Strain ◽  
Plane State ◽  
Elastic Plastic ◽  
Principal Strains

The paper presents an experimental method for the solution of the plane state of stress of an elastic-plastic, isotropic solid that obeys the Mises yield condition and the associated flow rule. The stress-strain law is an incremental type law, determined by the Prandtl-Reuss stress-strain relations. The method consists in determining the difference of principal strains in the plane of stress by using birefringent coatings cemented on the surface of the tested solid. A determination of relative retardation using polarized light at normal incidence, complemented by a determination in two oblique incidences at 45 deg along with the tracing of isoclinics, procures enough data for obtaining the principal strains all over the field. The calculation of the elastic and plastic components of strains is obtained in a step-by-step process of loading. It is assumed that during each step the Cartesian components of stress and strain remain constant. The stress increments and the stresses can be found thereafter by using the Prandtl-Reuss stress-strain relations and used for the evaluation of the components of strains and their increments in the next step. The method can be used with any material having any arbitrary stress-strain curve, provided that convenient formulas are established relating the stress and strain components and their increments at each point of the loading path. The method is applied to an example of contained plastic flow in a notched tensile bar of an elastic, perfectly plastic material under conditions of plane stress.

scholarly journals Strain Localization of Orthotropic Elasto–Plastic Cohesive–Frictional Materials: Analytical Results and Numerical Verification

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2040
Author(s):  
Sungchul Kim ◽  
Miguel Cervera ◽  
Jian-Ying Wu ◽  
Michele Chiumenti
Keyword(s):  
Plane Strain ◽  
Plastic Flow ◽  
Plane Stress ◽  
Strain Localization ◽  
Numerical Results ◽  
Flow Rule ◽  
Numerical Verification ◽  
Applied Loading ◽  
Analytical Results ◽  
Frictional Materials

Strain localization analysis for orthotropic-associated plasticity in cohesive–frictional materials is addressed in this work. Specifically, the localization condition is derived from Maxwell’s kinematics, the plastic flow rule and the boundedness of stress rates. The analysis is applicable to strong and regularized discontinuity settings. Expanding on previous works, the quadratic orthotropic Hoffman and Tsai–Wu models are investigated and compared to pressure insensitive and sensitive models such as von Mises, Hill and Drucker–Prager. Analytical localization angles are obtained in uniaxial tension and compression under plane stress and plane strain conditions. These are only dependent on the plastic potential adopted; ensuing, a geometrical interpretation in the stress space is offered. The analytical results are then validated by independent numerical simulations. The B-bar finite element is used to deal with the limiting incompressibility in the purely isochoric plastic flow. For a strip under vertical stretching in plane stress and plane strain as well as Prandtl’s problem of indentation by a flat rigid die in plane strain, numerical results are presented for both isotropic and orthotropic plasticity models with or without tilting angle between the material axes and the applied loading. The influence of frictional behavior is studied. In all the investigated cases, the numerical results provide compelling support to the analytical prognosis.

Improved Compliance Solutions for C(T), SE(B) and Clamped SE(T) Specimens Including Side-Grooves, Varying Thicknesses and 3-D Effects

2014 ◽  
Author(s):  
Gustavo Henrique B. Donato ◽  
Felipe Cavalheiro Moreira
Keyword(s):  
Crack Growth ◽  
Plane Strain ◽  
Plane Stress ◽  
Potential Drop ◽  
Crack Size ◽  
Growth Conditions ◽  
Size Estimation ◽  
Unloading Compliance ◽  
Integrity Assessments ◽  
Elastic Unloading

Fracture toughness and Fatigue Crack Growth (FCG) experimental data represent the basis for accurate designs and integrity assessments of components containing crack-like defects. Considering ductile and high toughness structural materials, crack growing curves (e.g. J-R curves) and FCG data (in terms of da/dN vs. ΔK or ΔJ) assumed paramount relevance since characterize, respectively, ductile fracture and cyclic crack growth conditions. In common, these two types of mechanical properties severely depend on real-time and precise crack size estimations during laboratory testing. Optical, electric potential drop or (most commonly) elastic unloading compliance (C) techniques can be employed. In the latter method, crack size estimation derives from C using a dimensionless parameter (μ) which incorporates specimen’s thickness (B), elasticity (E) and compliance itself. Plane stress and plane strain solutions for μ are available in several standards regarding C(T), SE(B) and M(T) specimens, among others. Current challenges include: i) real specimens are in neither plane stress nor plane strain - modulus vary between E (plane stress) and E/(1-ν2) (plane strain), revealing effects of thickness and 3-D configurations; ii) furthermore, side-grooves affect specimen’s stiffness, leading to an “effective thickness”. Previous results from current authors revealed deviations larger than 10% in crack size estimations following existing practices, especially for shallow cracks and side-grooved samples. In addition, compliance solutions for the emerging clamped SE(T) specimens are not yet standardized. As a step in this direction, this work investigates 3-D, thickness and side-groove effects on compliance solutions applicable to C(T), SE(B) and clamped SE(T) specimens. Refined 3-D elastic FE-models provide Load-CMOD evolutions. The analysis matrix includes crack depths between a/W=0.1 and a/W=0.7 and varying thicknesses (W/B = 4, W/B = 2 and W/B = 1). Side-grooves of 5%, 10% and 20% are also considered. The results include compliance solutions incorporating all aforementioned effects to provide accurate crack size estimation during laboratory fracture and FCG testing. All proposals revealed reduced deviations if compared to existing solutions.

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