# Variation of Fracture Toughness with Biaxial Load and T-Stress under Mode I Condition
###### Abstract  
The effect of a biaxial load on brittle fractures of solids under predominantly elastic deformation and mode I loading conditions is studied in this article. A cross-shaped specimen is used in this work, and the variation of T-stress is achieved by changing the load applied to the arm parallel to the crack. In the tests, under a series of different loads parallel to the crack, a series of load values perpendicular to the crack are obtained, and the stress intensity factor is calculated by FEM (Finite Element Analysis). The test data demonstrate that the apparent fracture toughness of the material varies with the load parallel to the crack and the T-stress, since the T-stress is directly related to the load parallel to the crack. If only the first term of the Williams series solution is used to describe the stress field near the crack tip, the variation of KC is unexplained; therefore, more than one term in the Williams series solutions is used to develop the theory of biaxial effect on solid fracture behavior. The fracture criterion based on this consideration is also used to predict crack instability or crack curving under mode I load conditions. Experimental data are presented and compared with the theory. T-stress; cross-shaped specimen; biaxial load; crack curving +
Footnote †: journal: Applied Physics Letters  
**Citation:** [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; Variation of Fracture Toughness with Biaxial Load and T-stress under Mode I Condition. Further developing the view of [PERSON] and [PERSON] [1], [PERSON] and [PERSON] [2] examined this constraint effect in the fracture of brittle materials and revisited the governing equations for both stress and strain in the vicinity of a crack tip in their research. In order to verify the constrained effect of the brittle material's fracture behavior, they used different shapes of specimens as test objects, including compact tension (CT), single-edge-notch in tension (SENT) and double cantilever beam (DCB) specimens. It is demonstrated that the critical stress intensity factor or apparent fracture toughness of PMMA (polymethyl methacrylate) varies with the specimen geometry or the constraint level. In the condition of uniaxial loading, different geometrical specimens were used in order to obtain different constraints, in the work by [PERSON] and [PERSON] [2]. However, in their experiment, the geometry of the specimen was limited, so that continuously varying constraints were difficult to exhibit. In view of the above problems, in this paper, we use the biaxially loaded cross-shaped specimens as the test objects, and directly control the constraint condition of the fracture event by changing the magnitude of the load parallel to the crack. The stress intensity factor K has been considered as not the only parameter affecting the fracture behavior in the brittle fracture [3], and whether the geometric shape, loading configuration and other factors can be uniformly expressed as the influence of T-stress on the fracture behavior is the key argument of this paper. It can be concluded from the test results that as the T-stress increases, the fracture toughness or critical fracture factor will increase; that is to say, \(K\) stress is not the only parameter affecting the brittle fracture behavior. Compared with the specimens with certain shape, the test with the cross-shaped specimen helps to obtain a series of continuously changing data points, which is more conducive to quantitative analysis and comparison with the theoretical model [4; 5; 6]. The control method of biaxial tensile testing machine can be referenced from these articles [7; 8; 9; 10; 11]. For the propagation behavior of mixed mode cracks under biaxial load, we may refer to the innovative ideas in these studies [12; 13; 14]. Although there are some differences in the propagation behavior between mixed-mode cracks and mode I cracks, the test methods adopted in these articles can provide useful reference for our research.