Effects of fiber cracking on elastoplastic-damage behavior of fiber-reinforced metal matrix composites

2012 ◽  
Vol 22 (1) ◽  
pp. 48-67 ◽  
Author(s):  
YF Ko ◽  
JW Ju
Keyword(s):  
Yield Criterion ◽  
Analytical Framework ◽  
Internal Stresses ◽  
Order Effects ◽  
Flow Rule ◽  
Fiber Reinforced ◽  
Elastoplastic Behavior ◽  
Hardening Law ◽  
Effective Yield ◽  
Elastoplastic Damage

A micromechanical multi-level elastoplastic evolutionary damage framework is proposed to predict the overall transverse mechanical behavior and damage evolutions of cylindrical fiber-reinforced ductile composites. Progressively cracked fibers are modeled using the double-inclusion theory. The effective elastic moduli of three-phase composites, consisting of a matrix, randomly located yet monotonically aligned cylindrical uncracked fibers and cracked fibers, are derived by using a micromechanical formulation. In order to characterize the homogenized elastoplastic behavior, a micromechanical effective yield criterion is derived based on the ensemble-area averaging process and the first-order effects of eigenstrains. The resulting effective yield criterion, together with the overall associative plastic flow rule and the hardening law, constitutes the analytical framework for the estimation of effective transverse elastoplastic-damage responses of ductile composites containing both uncracked and cracked fibers. An evolutionary fiber cracking process, governed by the internal stresses and the fracture strength of fibers, is incorporated into the proposed work. The Weibull’s probabilistic distribution is employed to describe the varying probability of fiber cracking. Further, systematic numerical simulations are presented to illustrate the potential of the proposed methodology.

Micromechanical Evolutionary Elastoplastic Damage Model for Fiber-Reinforced Metal Matrix Composites With Fiber Debonding

2004 ◽  
Author(s):  
J. W. Ju ◽  
H. N. Ruan ◽  
Y. F. Ko
Keyword(s):  
Metal Matrix Composites ◽  
Metal Matrix ◽  
Yield Criterion ◽  
Damage Model ◽  
Order Effects ◽  
Matrix Composites ◽  
Fiber Reinforced ◽  
Interfacial Damage ◽  
Elastoplastic Behavior ◽  
Three Phase

A micromechanical evolutionary damage model is proposed to predict the overall elastoplastic behavior and interfacial damage evolution of fiber-reinforced metal matrix composites. Progressive debonded fibers are replaced by equivalent voids. The effective elastic moduli of three-phase composites, composed of a ductile matrix, randomly located yet unidirectionally aligned circular fibers, and voids, are derived by using a rigorous micromechanical formulation. In order to characterize the overall elastoplastic behavior, an effective yield criterion is derived based on the ensemble-area averaging process and the first-order effects of eigenstrains.

Descriptions of Reversed Yielding in Internally Pressurized Tubes

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Sergei Alexandrov ◽  
Woncheol Jeong ◽  
Kwansoo Chung
Keyword(s):  
Yield Criterion ◽  
Numerical Technique ◽  
Kinematic Hardening ◽  
Material Model ◽  
Flow Rule ◽  
Hardening Material ◽  
Hardening Law ◽  
Solving Equations ◽  
Associated Flow Rule ◽  
Reversed Deformation

Using Tresca's yield criterion and its associated flow rule, solutions are obtained for the stresses and strains when a thick-walled tube is subject to internal pressure and subsequent unloading. A bilinear hardening material model in which allowances are made for a Bauschinger effect is adopted. A variable elastic range and different rates under forward and reversed deformation are assumed. Prager's translation law is obtained as a particular case. The solutions are practically analytic. However, a numerical technique is necessary to solve transcendental equations. Conditions are expressed for which the release is purely elastic and elastic–plastic. The importance of verifying conditions under which the Tresca theory is valid is emphasized. Possible numerical difficulties with solving equations that express these conditions are highlighted. The effect of kinematic hardening law on the validity of the solutions found is demonstrated.

ADAPTIVE INCREMENTAL FINITE ELEMENT PROCEDURE FOR SOLVING ELASTOPLASTIC FRICTIONAL CONTACT PROBLEMS SUBJECTED TO NORMAL AND TANGENTIAL LOADS

2014 ◽  
Vol 06 (03) ◽  
pp. 1450031 ◽  
Author(s):  
W. S. ABDALLA ◽  
S. S. ALI-ELDIN ◽  
M. R. GHAZY
Keyword(s):  
Finite Element ◽  
Frictional Contact ◽  
Programming Model ◽  
Yield Criterion ◽  
Contact Problems ◽  
Flow Rule ◽  
Friction Behavior ◽  
Elastoplastic Behavior ◽  
Coulomb’S Friction ◽  
Von Mises

This paper presents a numerical model for analyzing the stresses and displacements of deformable bodies in contact with the presence of friction and material nonlinearity. Based on the finite element method (FEM), the elastoplastic frictional contact problem is formulated as an incremental convex programming model (ICPM) under inequality contact constraints and friction conditions. The classical Coulomb's friction law and the Prandtl–Reuss flow rule with the von Mises yield criterion are used to simulate the interface friction conditions and the elastoplastic behavior of the contacting bodies, respectively. The Lagrange multiplier approach is adopted for imposing the contact constraints. Furthermore, an effective adaptive incremental procedure is developed for solving the elastoplastic frictional contact problems. Examples for the frictional contact having advancing and receding nature are analyzed. The obtained results prove the ability of the developed procedure to investigate the sequence of different events during monotonic application of external loads. In addition, the results elucidate the effect of external side force on the friction behavior in the presence of plastic deformation. Good agreement has been found with published results.

A Constitutive Model with Effect of Temperature for Frozen Soil

2014 ◽  
Vol 919-921 ◽  
pp. 627-631 ◽  
Author(s):  
Xiang Tian Xu ◽  
Cai Xia Fan ◽  
Tian Yu Zhang
Keyword(s):  
Constitutive Model ◽  
Yield Criterion ◽  
Frozen Soil ◽  
Effect Of Temperature ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Model Coupling ◽  
Hardening Law ◽  
Different Temperatures ◽  
Temperature Variable

To model the stress-strain relation of frozen soil under different temperatures, an elasto-plastic constitutive model coupling with temperature variable was proposed. Under axisymmetric condition, elastic strain was calculated by the K-G model coupling with temperature. The plastic strain was calculated by using the DP yield criterion, associated flow rule and isotropic hardening law. All of the elastic and plastic parameters are related to the temperature variable. The simulated results show that the proposed model can predict the deformation behavior of frozen soil under different temperatures.

The Shrink Fit with Nonlinearly Hardening Elastic-Plastic Hub

1987 ◽  
Vol 54 (2) ◽  
pp. 474-476 ◽  
Author(s):  
Udo Gamer
Keyword(s):  
Yield Criterion ◽  
Elastic Region ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Hardening Law ◽  
Elastic Disk ◽  
Shrink Fit ◽  
Associated Flow Rule ◽  
Nonlinear Hardening

Based on Tresca’s yield criterion and the associated flow rule, stresses and displacement in a rotating shrink fit consisting of an elastic disk and a partially plasticized annulus are calculated for an arbitrary nonlinear hardening law. It is shown that the elastic-plastic border radius and the stresses in the elastic region of the hub do not depend on the hardening law.

Analytical Solution for Elastic and Elastoplastic Bending of a Curved Beam Composed of Inhomogeneous Materials

2013 ◽  
Vol 535-536 ◽  
pp. 353-356 ◽  
Author(s):  
Guo Jun Nie ◽  
Zheng Zhong
Keyword(s):  
Stress State ◽  
Analytical Solution ◽  
Numerical Solutions ◽  
Yield Criterion ◽  
Flow Rule ◽  
Curved Beam ◽  
Power Functions ◽  
Inhomogeneous Materials ◽  
Elastoplastic Behavior ◽  
Elastoplastic Bending

We present an analytical solution for elastic and elastoplastic bending problem of a curved beam composed of inhomogeneous materials. Suppose the material is isotropic, ideally elastoplastic and it obeys Tresca’s yield criterion and the corresponding associated flow rule. And the elastic modulus and yield limit of the material vary radially according to general power functions. The expressions of stresses and displacements of a curved beam in both purely elastic stress state and partially plastic stress state are derived. The influence of material inhomogeneity on the elastoplastic behavior of a curved beam is demonstrated in numerical examples. Analytical solutions presented here can serve as benchmark results for evaluating numerical solutions.

Stress Analysis of Thin Elasto-Plastic Shells

1971 ◽  
Vol 93 (3) ◽  
pp. 851-861 ◽  
Author(s):  
Oles Lomacky ◽  
Barry Hyman
Keyword(s):  
Stress Analysis ◽  
Yield Criterion ◽  
Strain Curve ◽  
Normal Displacement ◽  
Flow Rule ◽  
Stress And Strain ◽  
Stress Strain Curve ◽  
Hardening Law ◽  
Concentration Factors ◽  
Special Case

The stress analysis of thin shells with large deflections loaded into the strain hardening range is presented. Plastic strain incompressibility is assumed. The two governing differential equations in terms of the stress function and the normal displacement are derived in a form where the corresponding equations of the elastic problem are modified only by the addition of the integrals of the plastic strains. The equations can be utilized in conjunction with any yield criterion, flow rule, and hardening law. The theory is applied to the problem of stress concentration around a circular opening in a pressurized spherical shell. A numerical solution is obtained by an iterative procedure using the finite difference technique for the special case of small displacements, bilinear stress strain curve, and deformation theory of plasticity. The speed of convergence for plastic stress and strain concentration factors was found to decrease with increasing pressure.

scholarly journals Description of the Expansion of a Two-Layer Tube: An Analytic Plane-Strain Solution for Arbitrary Pressure-Independent Yield Criterion and Hardening Law

Metals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 793
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Lihui Lang
Keyword(s):  
Plane Strain ◽  
Special Functions ◽  
Yield Criterion ◽  
Practical Importance ◽  
Constitutive Parameter ◽  
Radial Coordinate ◽  
Flow Rule ◽  
Hardening Law ◽  
Lagrangian Coordinate ◽  
Pressure Independent

The main objective of the present paper is to provide a simple analytical solution for describing the expansion of a two-layer tube under plane-strain conditions for its subsequent use in the preliminary design of hydroforming processes. Each layer’s constitutive equations are an arbitrary pressure-independent yield criterion, its associated plastic flow rule, and an arbitrary hardening law. The elastic portion of strain is neglected. The method of solution is based on two transformations of space variables. Firstly, a Lagrangian coordinate is introduced instead of the Eulerian radial coordinate. Then, the Lagrangian coordinate is replaced with the equivalent strain. The solution reduces to ordinary integrals that, in general, should be evaluated numerically. However, for two hardening laws of practical importance, these integrals are expressed in terms of special functions. Three geometric parameters for the initial configuration, a constitutive parameter, and two arbitrary functions classify the boundary value problem. Therefore, a detailed parametric analysis of the solution is not feasible. The illustrative example demonstrates the effect of the outer layer’s thickness on the pressure applied to the inner radius of the tube.

Plane-Strain Crack-Tip Fields for Pressure-Sensitive Dilatant Materials

1990 ◽  
Vol 57 (1) ◽  
pp. 40-49 ◽  
Author(s):  
F. Z. Li ◽  
J. Pan
Keyword(s):  
Plane Strain ◽  
Effective Stress ◽  
Hydrostatic Stress ◽  
Yield Criterion ◽  
Crack Tip ◽  
Flow Rule ◽  
Pressure Sensitivity ◽  
Crack Tip Fields ◽  
Pressure Sensitive ◽  
Plane Strain Crack

Plane-strain crack-tip stress and strain fields are presented for materials exhibiting pressure-sensitive yielding and plastic volumetric deformation. The yield criterion is described by a linear combination of the effective stress and the hydrostatic stress, and the plastic dilatancy is introduced by the normality flow rule. The material hardening is assumed to follow a power-law relation. For small pressure sensitivity, the plane-strain mode I singular fields are found in a separable form similar to the HRR fields (Hutchinson, 1968a, b; Rice and Rosengren, 1968). The angular distributions of the fields depend on the material-hardening exponent and the pressure-sensitivity parameter. The low-hardening solutions for different degrees of pressure sensitivity are found to agree remarkably with the corresponding perfectly-plastic solutions. An important aspect of the effects of pressure-sensitive yielding and plastic dilatancy on the crack-tip fields is the lowering of the hydrostatic stress and the effective stress directly ahead of the crack tip, which may contribute to the experimentally-observed enhancement of fracture toughness in some ceramic and polymeric composite materials.

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