A Hardening Rule Between Stress Resultants and Generalized Plastic Strains for Thin Plates of Power-Law Hardening Materials

1993 ◽  
Vol 60 (2) ◽  
pp. 548-554 ◽  
Author(s):  
C. H. Chou ◽  
J. Pan ◽  
S. C. Tang
Keyword(s):  
Plastic Strain ◽  
Power Law ◽  
Potential Surface ◽  
Equivalent Stress ◽  
Yield Function ◽  
Constitutive Law ◽  
Thin Plates ◽  
Plastic Strain Rate ◽  
Hardening Rule ◽  
Stress Resultant

For power-law hardening materials, a stress resultant constitutive law of incremental plasticity nature for thin plates is constructed. The yield function in the stress resultant space is approximated in quadratic form and an equivalent stress resultant is defined. One of two parameters in the yield function is analytically determined based on the concept of complementary potential surface. The other is determined by the least square method to fit the complementary potential surface of Chou et al., (1991). In analogy to the work of Hill (1979), the equivalent work-conjugate generalized plastic strain rate is derived. Finally, the hardening rule between the equivalent stress resultant and generalized plastic strain is obtained based on the results of Chou et al. (1991) for power-law materials under proportional straining conditions.

PSEUDO-STEADY INDENTATION CREEP

2010 ◽  
Vol 24 (01n02) ◽  
pp. 227-237 ◽  
Author(s):  
HIDENARI TAKAGI ◽  
MING DAO ◽  
MASAMI FUJIWARA
Keyword(s):  
Strain Rate ◽  
Power Law ◽  
Equivalent Stress ◽  
Equivalent Plastic Strain ◽  
Tensile Creep ◽  
Plastic Strain Rate ◽  
Indentation Creep ◽  
Element Simulation ◽  
Representative Points ◽  
Indentation Strain

Theoretical analysis and computational modeling have been performed to carry out constant-indentation strain rate tests. Results show that both the indentation pressure and indentation strain rate become constant after a lapse of loading time. Moreover, the finite element simulation reveals that the contour-line patterns of equivalent stress and equivalent plastic stain rate underneath a conical indenter evolve with geometrical self-similarity corresponding to indenter displacement. This finding confirms that pseudo-steady indentation creep occurs in the region beneath the indenter. We define representative points in the underlying material as those with equivalent stress equal to the indentation pressure divided by a constraint coefficient of 3. During the pseudo-steady indentation creep of a power-law material, the equivalent plastic strain rate at these points is proportional to the indentation strain rate for compatibility. These results point out that a constitutive equation for the tensile creep of a power-law material can be predicted by constant-indentation strain rate tests.

Indentation Creep Studies of Cross-linked Glassy Polymer Films

1993 ◽  
Vol 308 ◽  
Author(s):  
Kevin M. O'Connor ◽  
Pamela A. Cleveland
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Indentation Depth ◽  
Glassy Polymer ◽  
Equivalent Stress ◽  
Plastic Strain Rate ◽  
Indentation Creep ◽  
Characteristic Relaxation Time ◽  
Depth Sensing ◽  
Creep Flow

ABSTRACTIndentation creep testing was done on cross-linked glassy polymers based on polystyrene, specifically poly(styrene-co-divinylbenzene) (PS-DVB) and poly(divinylbenzene) (PDVB). The continuous depth-sensing capabilities of the Nano-Indenter II were used to measure the time-dependent response to indentation at constant applied load. The raw creep data in terms of indentation depth vs time showed that PDVB was about 20% more resistant to penetration than PS-DVB. A data analysis program was developed that converted the raw data to stress σ and plastic strain rate ε and generated the plastic flow curve that was observed to follow the power law . The stress exponent a for PS-DVB increased with applied loads between 1 and 27 mN and was generally larger in magnitude than the exponent for PDVB. When compared at equivalent stress and indentation depth, the plastic strain rate for PDVB was observed to be about 100 times slower than for PS-DVB. This was attributed to the higher degree of cross-linking increasing the characteristic relaxation time governing creep flow in these polymers.

Nonlinear Analysis of Piercing Rolling Process by Element-Free Galerkin Method

2010 ◽  
Vol 26-28 ◽  
pp. 285-288
Author(s):  
Jian Hua Hu ◽  
Yuan Hua Shuang
Keyword(s):  
Plastic Strain ◽  
Galerkin Method ◽  
Equivalent Stress ◽  
Equivalent Plastic Strain ◽  
Rolling Process ◽  
Plastic Strain Rate ◽  
Element Free Galerkin Method ◽  
Rigid Plastic ◽  
Element Free Galerkin ◽  
Element Free

During piercing rolling simulation, extreme mesh deformation cannot be solved by the finite element method (FEM). Re-meshing is necessary to prevent the effect of severe mesh distortion. However, the element-free method can solve this problem because the continuous body is discretized with a set of nodes, not meshes. In this paper, three-dimension rigid-plastic element-free Galerkin Method (EFG) is introduced to analyze the piercing rolling process. The approximation functions are calculated considering a moving least squares (MLS) approach. The Newton-Raphson method is used for the solution of the nonlinear system of equations. The equivalent stress, the equivalent plastic strain and the equivalent plastic strain rate obtained by EFG and rigid-plastic FEM are analyzed and compared. The simulation results of the EFG method are in agreement with those obtained by using the rigid-plastic FEM and the effectiveness of the model is verified.

Stress update algorithm for non-associated flow metal plasticity

2012 ◽  
Vol 3 (2) ◽  
pp. 106-110
Author(s):  
Mohsen Safaei ◽  
Wim De Waele
Keyword(s):  
Plastic Strain ◽  
Yield Stress ◽  
Kinematic Hardening ◽  
Quadratic Function ◽  
Yield Function ◽  
Plastic Strain Rate ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Strain Rate Tensor ◽  
Incremental Change

. In this paper we present the continuum plasticity model based on non-Associated Flow Rule (nonAFR) for Hill’s48 quadratic yield function. In case of non-AFR, Hill’s quadratic function used as plasticpotential function, makes use of plastic strain ratios to determine the direction of effective plastic strain rate.In addition, the yield function uses direction dependent yield stress data. Therefore more accuratepredictions are expected in terms of both yield stress and strain ratios at different orientations. Weimplemented a modified version of the non-associative flow rule originally developed by Stoughton [1] intothe commercial finite element code ABAQUS by means of a user material subroutine UMAT. The mainalgorithm developed includes combined effects of isotropic and kinematic hardening [2]. This paper assumesproportional loading cases and therefore only isotropic hardening effect is considered. In our model theincremental change of plastic strain rate tensor is not equal to the incremental change of the compliancefactor. The validity of the model is demonstrated by comparing stresses and strain ratios obtained from finiteelement simulations with experimentally determined values for deep drawing steel DC06. A criticalcomparison is made between numerical results obtained from AFR and non-AFR based models.

scholarly journals An efficient and robust VUMAT implementation of elastoplastic constitutive laws in Abaqus/Explicit finite element code

2018 ◽  
Vol 19 (3) ◽  
pp. 308 ◽  
Author(s):  
Lu Ming ◽  
Olivier Pantalé
Keyword(s):  
Finite Element ◽  
Plastic Strain ◽  
Constitutive Laws ◽  
Constitutive Law ◽  
Computational Time ◽  
Plastic Strain Rate ◽  
Integration Scheme ◽  
Elastoplastic Material ◽  
Finite Element Software ◽  
Return Mapping

This paper describes the development of an efficient and robust numerical algorithm for the implementation of elastoplastic constitutive laws in the commercial non-linear finite element software Abaqus/Explicit through a VUMAT FORTRAN subroutine. In the present paper, while the Abaqus/Explicit uses an explicit time integration scheme, the implicit radial return mapping algorithm is used to compute the plastic strain, the plastic strain rate and the temperature at the end of each increment instead of the widely used forward Euler approach. This more complex process allows us to obtain more precise results with only a slight increase of the total computational time. Corrector term of the radial return scheme is obtained through the implementation of a safe and robust Newton–Raphson algorithm able to converge even when the piecewise defined hardening curve is not derivable everywhere. The complete method of how to implement a user-defined elastoplastic material model using the radial return mapping integration scheme is presented in details with the application to the widely used Johnson–Cook constitutive law. Five benchmark tests including one element tests, necking of a circular bar and 2D and 3D Taylor impact tests show the efficiency and robustness of the proposed algorithm and confirm the improved efficiency in terms of precision, stability and solution CPU time. Finally, three alternative constitutive laws (the TANH, modified TANH and Bäker laws) are presented, implemented through our VUMAT routine and tested.

A Criterion for Low-Cycle Fatigue Failure Under Biaxial States of Stress

1981 ◽  
Vol 103 (1) ◽  
pp. 1-6 ◽  
Author(s):  
D. Lefebvre ◽  
K. W. Neale ◽  
F. Ellyin
Keyword(s):  
Plastic Strain ◽  
Low Cycle Fatigue ◽  
Equivalent Stress ◽  
Equivalent Plastic Strain ◽  
Yield Function ◽  
Plastic Strain Amplitude ◽  
Multiaxial Fatigue ◽  
Cycle Fatigue ◽  
Stress Ratios ◽  
Von Mises

The plastic strain energy required for failure in low-cycle biaxial fatigue is estimated using the energy in uniaxial fatigue and assumptions from the theory of plasticity. A criterion for high-strain multiaxial fatigue of the form Δε¯pΔσ¯=KNƒc is developed, where the equivalent stress amplitude Δσ and the equivalent plastic strain amplitude Δεp are based on the von Mises yield function of plasticity. The parameters K and c are assumed to depend on the mechanical properties of the material and to be functions of the stress ratio. These functions can be evaluated from uniaxial fatigue data and are compared with tests performed on thin-walled tubes of mild steel at different stress ratios. The proposed criterion seems to yield a promising approach for the low-cycle fatigue analysis of metals under biaxial states of stress.

Longitudinal Impact on Viscoplastic Rods—Linear Stress-Strain Rate Law

1964 ◽  
Vol 31 (2) ◽  
pp. 199-207 ◽  
Author(s):  
T. C. T. Ting ◽  
P. S. Symonds
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Constitutive Law ◽  
Plastic Strain Rate ◽  
Longitudinal Impact ◽  
Plastic Strains ◽  
Stress Strain ◽  
Structural Metals ◽  
Rate Behavior ◽  
Strain Rate Behavior

Hohenemser and Prager [1] proposed a constitutive law for a solid of Bingham type We use a form of this law to study some cases of longitudinal impact on a bar causing large plastic strains. The results are intended to be of use in the design of impact tests on structural metals and in the interpretation of data from them, as well as helpful in guiding similar studies on materials with more complex plastic strain rate behavior.

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