Method for the determination of the characteristics of crack resistance of elastoplastic materials
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METHOD FOR THE DETERMINATION OF THE CHARACTERISTICS OF CRACK RESISTANCE OF ELASTOPLASTIC MATERIALS Ya. L. Ivanyts’kyi,1 S. Т. Shtayura,1,2 and M. Kowalik3
UDC 621.3
We propose a procedure for the determination of the level of strains, the length of the plastic zone, and crack-tip opening displacements based on the use of the digital speckle-correlation method and the data of strain-gauge measurements under the conditions of uniaxial and biaxial tension of a plate weakened by a central crack. It is experimentally established that the size of the plastic zone near the crack tip for a given material is independent of the gauge length but changes if we pass to biaxial loading. On the basis of the solution of the elastoplastic problem of limiting equilibrium of a plate weakened by a crack obtained within the framework of the δ c -model, we deduce the formula for the evaluation the mean value of crack resistance of the material (δ c ) and the length of the plastic zone (l p* ) . The influence of biaxial loading on the size of this zone is estimated. Keywords: crack-tip opening displacements, strains in the process zone, length of the plastic zone, digital correlation of speckle images, uniaxial and biaxial loading.
Introduction The deformation characteristics of the crack resistance of elastoplastic materials in the case where a plastic process zone is formed in the vicinity of the crack tip are found by using the δ c -model [1, 2]. In this case, the process zone is regarded as an additional model cut (crack) whose opposite sides are interacting (attracted to each other) due to the action of stresses σ 0 , and the critical crack opening displacements δ c on the line of the tip of the initial crack (2l0 ) [3] and at a certain distance from the tip are measured by strain gauges [4] (Fig. 1а). The critical crack opening displacement changes depending on the gauge length, i.e., with the distance between two points of the material in the vicinity of the crack tip. The crack resistance of the material is determined from the equality δ c = δ p* , where p = p* are the stresses caused by the action of a force P and p* is the level of stresses corresponding to the start of a crack of length 2l0 in the case of tension of the specimen (Fig. 1а). The stresses σ 0 in the δ c -model characterize the cohesive forces acting between the lips of the model crack in the process zone (in the zone l p in Fig. 1а) and are equal to the yield strength σ ys for perfectly elastoplastic materials or to σ 0 = (σ ys + σ u )/2 , where σ u is the ultimate strength of the material [5]. The procedure of finding δ c by measuring the displacements of points of the material in the vicinity of the crack tip with the help of strain gauges according to the well-known methods [2] is inefficient because the results depend on the gauge length [6]. 1
Karpenko Physicomechanical Institute, Ukrainian National Academy of Sciences, Lviv, Ukraine. Corresponding author; e-mail: [email protected]. 3 Technical University of Radom, Radom, Poland. 2
Translated from Fizyk
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