13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Experimental Observation and Constitutive Equations of Fracture Propagation Alexander Chudnovsky1, Zhenwen Zhou1, Haiying Zhang1,* 1 Department of Civil and Materials Engineering, University of Illinois at Chicago, 60607, USA * Corresponding author: haiyin@uic.edu Abstract There is a long list of empirical slow crack growth (SCG) equations that present the crack propagation rate as a function of stress intensity factor (SIF) or energy release rate (ERR). Experiments with crack growth through a heterogeneous stress field reveal the limitations of such type of equations resulting from existence of a process zone (PZ) surrounding the crack. PZ is a material “defense” against stress concentration caused by the crack and is commonly observed in most of engineering materials. It plays an important role in determination of the direction and rate of fracture propagation. Therefore, the PZ and crack are treated as two coupled elements of one Crack Layer (CL) system and CL propagation is represented by two coupled possesses: (i) the PZ evolution by transformation of the original material into a “damaged” and often anisotropic PZ material and (ii) crack growth into PZ. The CL driving forces are introduced as the negative derivative of Gibbs free energy with respect to CL geometrical parameters. The constitutive equations of CL propagation are formulated in form of simple relations between the crack and PZ growth rates and corresponding thermodynamic forces. Qualitative analysis of these equations suggests two distinctly different patterns of CL propagation: continuous and discontinuous, stepwise growth. A special experimental setup and test material have been selected to simplify and examine the proposed constitutive equations of CL growth. CL model provides a very good agreement with a large set of experimental data at various load levels, temperatures and specimen geometries. Keywords Crack layer model, slow crack growth, process zone, constitutive equations 1. Introduction Crack in engineering materials formed under fatigue and creep conditions usually appears as a narrow cut with small amplitude random deviations from a straight or slightly curved trajectory. A close observation of such crack reveals a presence of a process zone (PZ) (also called damage zone, plastic deformation zone, etc.) that precedes and surrounds the crack. Depending on material chemical composition and morphology, temperature, loading rate, specimen geometry, etc. various types of micro defects such as crazes, shear bands, microcracks, micro-voids constitute PZ. In general, microdefects are strain localizations on micro scale and based on their orientation one can distinguish brittle, such as crazes and micro-cracks, and ductile like shear bands and micro-voids, types of damage. The micro-defects are commonly formed in response to stress concentration, and shield the vicinity of the crack front from high elastic stresses by increase of an effective (inelastic) material compliance. The crack growth is closely coupled with formation and evolution of the micro-defects population within PZ. A system of coupled crack and PZ is referred to as Crack Layer (CL). There is a strong interaction between micro-defects in a vicinity of the crack front and the crack [1– 4]. It results in significant modification of the crack tip fields. Apparently, it also affects the stress intensity factor (SIF) K. Figure 1 illustrates the effect of micro-cracking (displacement discontinuities) on SIF. An individual micro-crack is modeled as a displacement discontinuity across an elementary segment (area in 3D) with orientation n and displacement jump b. In the specific example shown in Figure 1 all micro-cracks are considered to be parallel to the crack and have opening in the normal direction. The arrays of curves emanating from the crack tip forward and backward present contours of equal level of the mode I SIF Green’s function G1 SIF( ) due to unit normal displacement dipole with n(0,1) and b(0,1) at the point [3–5]. The continuous lines indicate SIF amplification effect due to the discontinuities located on the lines in front of the crack; whereas the two “butterfly wings” of dotted lines show the reduction of SIF, i.e., shielding effect of the discontinuities located on the lines
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