Singular rigid/plastic solutions in anisotropic plasticity under plane strain conditions

Continuum Mech. Thermodyn.

Kuo

Jeng

2015

Using the classical model of rigid perfectly plastic solids, the strain rate intensity factor has been previously introduced as the coefficient of the leading singular term in a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. Since then, many strain rate intensity factors have been determined by means of analytical and semi-analytical solutions. However, no attempt has been made to develop a numerical method for calculating the strain rate intensity factor. This paper presents such a method for planar flow. The method is based on the theory of characteristics. First, the strain rate intensity factor is derived in characteristic coordinates. Then, a standard numerical slip-line technique is supplemented with a procedure to calculate the strain rate intensity factor. The distribution of the strain rate intensity factor along the friction surface in compression of a layer between two parallel plates is determined. A high accuracy of this numerical solution for the strain rate intensity factor is confirmed by comparison with an analytic solution. It is shown that the distribution of the strain rate intensity factor is in general discontinuous.

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

A numerical method for determining the strain rate intensity factor under plane strain conditions

Continuum Mech. Thermodyn.

Kuo

Jeng

2015

“…In the case of rigid perfectly plastic solids, the maximum friction surface is defined by the condition that the friction stress at sliding is equal to the shear yield stress. The main result obtained in [1] has been extended to the double shearing model and a model of anisotropic plasticity in [2,3], respectively. A description of the double shearing model is given in [4] and the model of anisotropic plasticity in [5].…”

Section: Introductionmentioning

confidence: 97%

Quasi-static axially symmetric viscoplastic flows near very rough walls

Applied Mathematical Modelling

Mustafa

2015

Self Cite

a b s t r a c tThe paper deals with asymptotic behavior of viscous and viscoplastic solutions in the vicinity of very rough walls under conditions of axial symmetry. The constitutive equations adopted include a saturation stress. A distinguished feature of this model is that the regime of sticking at the wall may be incompatible with other boundary conditions. In this case the regime of sliding must occur and solutions are singular in the vicinity of such surfaces. The exact asymptotic representation of the singular solutions is controlled by the dependence of the equivalent stress on the equivalent strain rate as the latter approaches infinity. There exist such dependences that the viscoplastic model possesses a smooth transition of qualitative behavior between rigid perfectly plastic and viscoplastic solutions, and this may prove to be advantageous for some applications.

“…The theory of anisotropic plasticity developed in [20] is adopted. It has been demonstrated in [7] that Eq. (1) is valid in this case.…”

Section: Introductionmentioning

confidence: 97%

“…All of the aforementioned models are for isotropic materials. It has been recently proven in [7] that the strain rate intensity factor can be introduced in plane strain problems of anisotropic plasticity based on quite a general yield criterion and its associated flow rule. However, no specific solutions for the strain rate intensity factor have been proposed.…”

Section: Introductionmentioning

confidence: 99%

The strain rate intensity factor in the plane strain compression of thin anisotropic metal strip

Mustafa

2014

Meccanica

Self Cite

Using an available analytic solution for instantaneous plane strain compression of a plastically anisotropic strip between two parallel plates the strain rate intensity factor is found assuming Hill's quadratic yield criterion. The distribution of material properties is uniform. The effect of parameters characterizing plastic anisotropy of the strip on the magnitude of the strain rate intensity factor is demonstrated. A possibility to replace the strain rate intensity factor with the plastic work rate intensity factor is discussed. Singular behavior of the plastic spin in the vicinity of the friction surface is revealed and discussed.