Application of the Unified Strength Theory in Analyzing Fracture Strength

Abstract

In practical engineering, the cracks are always mixed mode. The research on the mixed fracture criterion has an important significance in fracture mechanics and engineering. Stress state of the mixed mode cracks is complicated. A new unified strength theory considering the effects of all the three principal stresses is generalized into the fracture mechanics in this paper. The complex stress states are common characteristics between the mixed mode cracks and the unified strength theory. A unified fracture function criterion is established by using the unified strength theory in this paper. In the unified fracture function, the difference between tension and pressure and the effect of the intermediate principal stress σ2are considered. With the variation of α = σt/ σcand failure parameter b , a series of mixed mode crack criteria are formed, and can be applied for many materials. The J-integral is calculated through FEM. According to the relation between the result and the stress intensity factor, Klccan be obtained. Then it is used in the unified fracture function. The unified fracture criterion is compared with those of other mixed mode criterions.

Generalized Plasticity

“…They are: Unified Strength Theory ; Unified Slip Line Field Theory for Plane Strain Problem ; Unified Characteristics Field Theory for Plane Stress Problem Zhang, 1998, 1999;Zhang, Hao and Yu, et al, 2003); Unified Characteristics Field Theory for Spatial Axisymmetric Problem (Yu and Li, 2001); Unified Solution for Limit Pressure of a Pressure Vessel (Wang and Fan, 1998;Zhao et al, 1999); Unified Solution for Shakedown Pressure of a Pressure Vessel Yu, 2004, 2005); Analysis of Plastic Zone at Crack Tip (Qiang et al, 1998(Qiang et al, , 2004; Unified Fracture Criterion (Yu, Fan, Che, Yoshimine, et al, 2003Qiang and Yu, 2004). The beauty of the unified strength theory discussed in Chap.…”

“…A unified fracture criterion was established by using the unified strength theory by Che et al in 2003 and In the unified fracture function, the difference between tension and pressure, the effect of the intermediate principal stress 2 σ and the effect of the intermediate principal shear-stress 12 (or 23 ) are taken into account. With the variation of θ π τ r K yz = (14-16)…”

“…They are all the special case of the plastic core region responses of the generalized T-criterion. A unified fracture criterion based directly on the unified strength theory was obtained by Yu, Fan, Che et al in 2003 In this chapter, a variable radius for the plastic core region based on the UST elastic-plastic boundary is introduced and incorporated in the formulation of the T-criterion, the lower bound and upper bound plastic core region responses of T-criterion is derived. Comparisons of the three particular solutions with respect to the Tresca-core region, the Huber-von Mises-core region and the TS-core region are made mutually.…”

“…It is introduced directly from the formulation of the unified strength theory (Fan 2003, Yu, Fan and Che 2003. The relations of crack initial angle with unified strength parameter b for mode crack ( ~ ~b curves), cracked initial angle with various fracture criteria, unified fracture criterion of mixed I-II mode for various α , unified fracture criterion of mixed I-III mode for various α , and the unified fracture criterion of mixed II-III mode for various α are obtained by using the numerical calculation method.…”

Plastic Failure Analysis of Roadway Floor Surrounding Rocks Based on Unified Strength Theory

“…For example, Zhao et al [17][18][19] studied complex elastoviscoplastic behaviors of rock subjected to triaxial stress state and proposed a new EVP creep model to study timedependent change in the plastic zone. In 1985, Yu et al [20,21] put forward a unified strength theory and a double shear strength theory based on the concept of double shear. Under the condition of hydrostatic pressure, the elasticplastic distribution of the circular roadway obtained by the unified strength theory is analyzed.…”