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Interrelation Between Constitutive Laws and Fracture in the Vicinity of Friction Surfaces
Abstract It is well known that cracks can produce stress singularities in linear elastic materials. One common type of stress singularity is $$ \sigma \propto K/\sqrt r $$ where r is the distance from the crack tip and K is the stress intensity factor. The stress intensity factor approach is very effective in structural design. In particular, a popular fracture criterion is formulated in the form K = K c where K c is a critical value of the stress intensity factor, a material constant. In the present paper the general concept of the stress intensity factor is adopted for fracture analysis in the vicinity of maximum friction surfaces (surfaces where the frictional stress attains its maximum possible value). The basic constitutive law is the rigid/perfectly plastic solid. In this case the equivalent strain rate, ξ eq , is describable by nondifferentiable functions in the vicinity of maximum friction surfaces and its behavior is given by $$ \xi _{eq} \propto D/\sqrt {x_3 } $$ where x 3 is the distance from the friction surface. Most fracture criteria in metal forming involve the equivalent strain rate in such a manner that they would immediately predict fracture initiation at the maximum friction surface since the behavior of a fracture parameter is singular and its value approaches infinity at the friction surface. Therefore, by analogy with the mechanics of cracks, it is natural to assume that the intensity of the strain rate singularity can be used to predict fracture in the vicinity of maximum friction surfaces. In the present paper the equivalent strain is used as the fracture parameter. The strain intensity factor E, which controls the magnitude of the equivalent strain in the vicinity of a maximum friction surface, is introduced and then a fracture criterion is postulated in the form E — E c where E c is assumed to be a material constant. The effects of temperature, pressure dependence of the yield condition, viscosity, and strain hardening on the behavior of solution in the vicinity of the maximum friction surface are discussed. A few examples are proposed to illustrate the approach.
Interrelation Between Constitutive Laws and Fracture in the Vicinity of Friction Surfaces
Abstract It is well known that cracks can produce stress singularities in linear elastic materials. One common type of stress singularity is $$ \sigma \propto K/\sqrt r $$ where r is the distance from the crack tip and K is the stress intensity factor. The stress intensity factor approach is very effective in structural design. In particular, a popular fracture criterion is formulated in the form K = K c where K c is a critical value of the stress intensity factor, a material constant. In the present paper the general concept of the stress intensity factor is adopted for fracture analysis in the vicinity of maximum friction surfaces (surfaces where the frictional stress attains its maximum possible value). The basic constitutive law is the rigid/perfectly plastic solid. In this case the equivalent strain rate, ξ eq , is describable by nondifferentiable functions in the vicinity of maximum friction surfaces and its behavior is given by $$ \xi _{eq} \propto D/\sqrt {x_3 } $$ where x 3 is the distance from the friction surface. Most fracture criteria in metal forming involve the equivalent strain rate in such a manner that they would immediately predict fracture initiation at the maximum friction surface since the behavior of a fracture parameter is singular and its value approaches infinity at the friction surface. Therefore, by analogy with the mechanics of cracks, it is natural to assume that the intensity of the strain rate singularity can be used to predict fracture in the vicinity of maximum friction surfaces. In the present paper the equivalent strain is used as the fracture parameter. The strain intensity factor E, which controls the magnitude of the equivalent strain in the vicinity of a maximum friction surface, is introduced and then a fracture criterion is postulated in the form E — E c where E c is assumed to be a material constant. The effects of temperature, pressure dependence of the yield condition, viscosity, and strain hardening on the behavior of solution in the vicinity of the maximum friction surface are discussed. A few examples are proposed to illustrate the approach.
Interrelation Between Constitutive Laws and Fracture in the Vicinity of Friction Surfaces
Alexandrov, S. (author)
2001-01-01
12 pages
Article/Chapter (Book)
Electronic Resource
English
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