Nov 01, 2015 read the elastostatic plane strain mode i crack tip stress and displacement fields in a generalized linear neohookean elastomer, journal of the mechanics and physics of solids on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. The characteristics of selected triaxiality measures of. Plastic orthotropy is described by hills quadratic yield function. A noteworthy feature of the solution is the rapid rise of triaxial stress concentration above the flow stress with increasing values of the hardening exponent. Rices 1973 general study of plane strain slip line theory for anisotropic rigidplastic materials see also booker and davis 1972.
Plane strain deformation near a crack tip in a power law hardening material, j. The analogous antiplane shear case was presented in part i rice and saeedvafa. The elasticplastic mechanics of crack extension solid mechanics. Mechanics of materials 5 1986 299316 299 northholland planestrain cracktip fields for powerlaw hardening orthotropic materials jw pan department of mechanical enginccring and applied mechanics, the university of michigan, ann arbor, all 48109, u. Finite element analysis of the stress and deformation. The finite antiplane shear field near the tip of a crack for a class of incompressible elastic solids.
Rosengren, plane strain deformation near a crack tip in a power law hardening material. The characteristics of selected triaxiality measures of the. The anti plane shear elastostatic fields near a crack terminating at an isotropic hyperelastic bi material interface. In view of the near tip constraint effect imposed by the geometry and loading configuration, a creep fracture analysis based on c only is generally not sufficient. Strainhardening plays an important role of producing unique stress and strain. In the outofplane direction, generalized plane strain is imposed such that the outofplane axial strain is constant throughout the domain and given by zz 1 e s. The perfect elasticviscoplastic field at mode i quasistatic. Dynamic crack propagation 685 called the plane stress dynamic fracture toughness. Effects of the strainhardening exponent on twoparameter. In this article, special emphasis is laid on the wellknown irwins solution of elastic material. Plane strain deformation near a crack tip in a powerlaw hardening.
Fong shih division of engineering brown university providence, ri 02912, u. Read the elastostatic plane strain mode i crack tip stress and displacement fields in a generalized linear neohookean elastomer, journal of the mechanics and physics of solids on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Detailed investigation of constraint effects on neartip. Tranb a lehrstuhl fur mechanik materialtheorie, ruhruniversitat bochum, d44780 bochum, germany b department of mechanics, faculty of mathematics and computer science, ho chi minh university of science, viet nam abstract within the continuum dislocation theory the asymptotic analysis of the plane. Finite element analysis of the stress and deformation fields around the blunting crack tip is considered to be a function of the equivalent plastic strain p. The angular variations of these hrrtype fields depend on a single parameter which specifies the. Pdf plane strain deformation near a crack tip researchgate. The characterization of the stress fields near a crack tip. Hutchinson 1968 and rice and rosengren 1968 proposed the wellknown hrr singular. Then, in a fascinating, pioneering paper that has caused a burst of interest in this subject, rice 1987 published an asymptotic study of crack tip stress and deformation elds for plane strain tensile cracks in. It is shown in this note that for incompressible elasticplastic material hardening according to a power law, the dynamic near tip fields can be expressed in a simple form in terms of the corresponding nonlinear static fields and. Plastic deformation precedes fracture in metals and their alloys and resistance to.
Plane strain deformation near crack tip in a power law hardening materials. This paper describes an asymptotic analysis of the strain and stress fields at the tip of a crack in a sheet of incompressible hyperelastic material. Finite element analysis of the stress and deformation fields. Finite element analysis of the stress and deformation fields around the blunting. On higherorder cracktip fields in creeping solids journal. Journal of the mechanics and physics of solids vol. Stress and dislocation distributions near a crack tip in. Both the symmetric mode i and nonsymmetric mixedmode cases are considered. Near crack tip plane strain singularities may be found for incompressible. Tstress in elasticplastic cracktip fields springerlink. Hydrogenenhanced localized plasticity help is recognized as.
An experimental study of the eect of hardening on plastic. Numerical procedure the problem considered in this study is a. The perfect elasticviscoplastic field at mode i quasi. A ligament field ahead of a crack tip for modeli plane strain problem in a power law hardening material is developed. Jr rice gf rosengren 1968 articletitle plane strain deformation near a crack tip in a power law hardening material j mech phys solids 16 112 occurrence handle 0166. Asymptotic solutions for tensile crack tip elds without. Ratcheting strain can be defined as the mean strains of a hysteresis loop, ie, half of the summation of maximum and minimum strains of a loop. Within the limitations of a smallstrain, j2 deformation theory of plasticity, the amplitude of the above dominant singularity. Near tip stress and strain fields for power law hardening orthotropic materials under plane strain conditions are presented. Some issues such as the range of dominance of the asymptotic stress and deformation fields and the amount of nonproportional loading near the crack tip, which have received wide attention in the analogous plane strain problem, are examined. Plane stress and plane strain solutions for a crack in a homogeneous material as well as for. Finite deformation analysis of crack tip opening in. Rosengren, journal of mechanics and physics of solids 16 1968, 112. This paper presents a formulation of higherorder crack tip fields in steady power law creeping solids which can be derived from an asymptotic development of near tip fields analogous to that of sharma and aravas and yang et al.
The details of the stress distribution, though, will depend on the mechanism by which the crack blunts. The analogous anti plane shear case was presented in part i rice and saeedvafa. Pdf plane strain deformation near a crack tip in a powerlaw. Corresponding near crack tip stress and strain fields are obtained for the plane straining of an incompressible elasticplastic material hardening according to a power law. The work presented here considers the eect of hardening on these strain elds. Hutchinson, journal of mechanics and physics of solids 16 1968, 31. Finite strain stress fields near the tip of an interface crack between a soft incompressible elastic material and a rigid substrate. The dynamic fracture toughness is assumed to depend in a onetoone manner on the crack tip velocity.
A twoterm expansion of the solution in the near crack tip region is developed. This is because such smallscale yielding solutions may be obtained through a boundary layer approach rice 1967a, b in which actual boundary conditions are replaced by the requirement of an asymptotic. Plane strain deformation near a crack tip in a powerlaw hardening material, j. This functional dependence on velocity is expected to be a purely material characteristic. Finite strains at the tip of a crack in a sheet of hyperelastic material. In view of the neartip constraint effect imposed by the geometry and loading configuration, a creep fracture analysis based on c only is generally not sufficient. A crack at the interface between two powerlaw materials. Singular behaviours at the end of a tensile crack in a hardening material, j. Mcclintock, i190 and strain hardening neuber, 1961. A ligament field ahead of a crack tip for modeli plane strain problem in a powerlaw hardening material is developed.
Such characterizations, for both elastic materials and models of metal plasticity, invariably lead to predictions of unbounded strain. Hence, for mode iii, the jintegral is pathindependent for smallscale yielding. In the plane strain linear elastic case williams 1959. Corresponding near crack tip stress and strain fields are obtained for the plane straining of an incompressible elasticplastic material hardening. Rice j r and rosengren g f 1968 plane strain deformation near a crack tip in a powerlaw hardening material j. No such proof of the pathindependence of j is available for the in. Rice, who showed that an energetic contour path integral called j was independent of the path around a crack. Integral estimates for strainhardening materials in. The angular variations of these hrrtype fields depend on a single parameter which specifies the state of plastic orthotropy. Mechanics of materials 5 1986 299316 299 northholland plane strain crack tip fields for power law hardening orthotropic materials jw pan department of mechanical enginccring and applied mechanics, the university of michigan, ann arbor, all 48109, u.
Plane strain deformation near a crack tip in a powerlaw hardening material 3. The jintegral represents a way to calculate the strain energy release rate, or work per unit fracture surface area, in a material. This leads to an interpenetration anomaly england 1965. Neglecting the s and tstresses, the characteristic size of the plastic zone around the crack tip is approximated as. Thus, all the field quantity necessary for the elastoplastic analysis of fracture mechanics can be obtained in this paper. The fact that the value of the j integral rice, 1968a provides a measure of the intensity of the near tip field in this asymptotic solution has prompted some inves.
This paper presents a formulation of higherorder cracktip fields in steady powerlaw creeping solids which can be derived from an asymptotic development of neartip fields analogous to that of sharma and aravas and yang et al. Jun 14, 2018 for the plane strain conditions, the stress. The theoretical concept of jintegral was developed in 1967 by g. Journal of the mechanics and physics of solids, vol. Planestress cracktip fields for powerlaw hardening. Plane strain deformation near a crack tip in power law hardening material 3 dimensions of the problem. Singular behaviour at the end of a tensile crack in a hardening material. The j2deformation plasticity theory with power law hardening is used to describe the constitutive behavior of the continuum. Plane strain deformation near a crack tip in a powerlaw. Abstract as crack fronts in power law hardening materials are approached, the asymp. Blunting of a plane strain crack tip into a shape with. The characterization of the stress fields near a crack tip for a. Let denote the energy density of elastic material then considering a.
Traditional fracture mechanics techniques are founded upon analytical characterization of crack tip fields based on classical small strain solid mechanics concepts. Plane strain deformation near crack tip in a power law hardening material j. Finite element analysis of the plane strain cracktip. Journal of mechanics and physics of solids, 1968, 161. The plastic work hardening in the materials is assumed to follow a powerlaw, as is also assumed in the well know hrr description of the near tip stress. Rice 1988, the near crack tip singularity has an oscillatory singularity. The plastic deformation of materials is characterized by the j. Finite deformation analysis of crack tip opening in elastic. Plane strain deformation near a crack tip in powerlaw hardening material 3 dimensions of the problem.
The investigations are carried out within the framework of finite elastostatics and for the class of generalized neohookean materials. Finite element analysis of elasticplastic large deformation. Plane strain deformation near crack tip in a power law hardening materialj. An alternative formulation of the ritchieknottrice local fracture criterion. An asymptotic elastic plastic analysis in plane strain. Study of hardening and cyclic plastic behaviour around the. The antiplane shear elastostatic fields near a crack.
On the pathdependence of the jintegral near a stationary. Neartip stress and strain fields for powerlaw hardening orthotropic materials under planestrain conditions are presented. Bending modified j q theory and cracktip constraint. The elastostatic plane strain mode i crack tip stress and. Planestrain cracktip fields for powerlaw hardening. An approximation for a power law hardening material indicates that the maximum stresses near the blunted crack tip is much the same for a crack with vertices on the tip as for a smoothly blunted crack tip. Rice 1988, the near cracktip singularity has an oscillatory singularity. The stress intensity factor is a measure of the intensity of the stress and strain fields near a crack tip in linear elastic fracture mechanics. Williams, stress singularities resulting from various boundary conditions in angular corners of plates in tension, j appl mech, 1952, 19. Here, we present mode i planestress cracktip solutions for powerlaw hardening orthotropic materials to show the effects of strain hardening and plastic orthotropy on. A few attempts to investigate crack tip plasticity under dynamic loading conditions have recently been discussed.
Here, we present mode i plane stress crack tip solutions for power law hardening orthotropic materials to show the effects of strain hardening and plastic orthotropy on. Stress and dislocation distributions near a crack tip in ductile single crystals k. Finite strains at the tip of a crack in a sheet of. In this paper, an asymptotic elastoplastic analysis in plane strain deformation near a crack tip is established.
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