An improved semi-circular bend specimen for investigating mixed mode brittle fracture

Abstract

An edge cracked semi-circular specimen subjected to asymmetric three-point bend loading was suggested for investigating mixed mode fracture in brittle materials. Using finite element analysis, the crack parameters were obtained for various crack lengths and different locations of loading points. It was shown that by selecting appropriate positions for the loading points, full mode mixities from pure mode I to pure mode II could be achieved. Then, a series of fracture tests were conducted on PMMA using the proposed specimen. Very good agreement was found between the experimental results and those predicted from the generalized maximum tangential stress criterion.

Introduction

The presence of flaws and cracks are very often inevitable in engineering structures and components. The cracks can be generated during the manufacturing processes or due to cyclic loading or environmental causes, etc. Pure mode I and pure mode II are two modes of deformation that take place for a cracked component subjected to in-plane loading. In practical situations, the cracked structures sometimes experience mixed mode loading, i.e. a combination of mode I and II. Mixed mode brittle fracture is one of the common types of mechanical failure in cracked components made of brittle or quasi-brittle materials. Therefore, it is important to investigate the structural integrity of cracked components under mixed mode loading.

Several theoretical and experimental methods have been suggested by researchers for exploring mixed mode brittle fracture. While the experimental fracture studies on real components are often expensive and difficult, researchers prefer to conduct their experiments on laboratory specimens. However, appropriate fracture criteria are also required to correlate the experimental results obtained from the simple laboratory specimens to the fracture event in cracked structures under their complex service loading conditions. In order to validate a fracture criterion, researchers have to conduct a series of experiments on appropriate test materials by using suitable test specimens. PMMA (polymethylmethacrylate or Perspex) has been recognized as a favorite model material for conducting brittle fracture experiments. The brittle type of fracture at room temperature, the convenience of machining and introducing a sharp crack and the optical transparency (which allows direct observation of fracture path) are among the advantages of PMMA in brittle fracture experiments.

In addition to the choice of test material, a valid fracture test requires an appropriate test configuration. For mixed mode fracture experiments, a suitable test configuration should have simple geometry and loading condition, inexpensive preparation procedure, convenience of testing set up and also the ability of introducing complete combinations of mode I and mode II. Some of the test configurations proposed in literature for investigating mixed mode I/II fracture are briefly described here. Erdogan and Sih [1], Williams and Ewing [2] and Theocaris [3] used a rectangular plate containing an inclined center crack and subjected to a uniform far field tension in their mixed mode fracture studies. The asymmetrically loaded three or four-point bend specimens were also employed by researchers for investigating mixed mode brittle fracture [4], [5], [6], [7], [8], [9], [10], [11]. Disc type specimens including the centrally cracked Brazilian disk (BD) specimen and the semi-circular bend (SCB) specimen have been frequently employed for determining the mixed mode fracture resistance of various engineering materials such as rocks and PMMA [12], [13], [14], [15], [16], [17], [18], [19], [20]. The compact tension-shear specimen [21], [22], [23] is another configuration used for mixed mode fracture experiments. Ewing et al. [24] also made use of the inclined edge-crack plates subjected to far field tension and bending to study mixed mode fracture in PMMA. More recently Ayatollahi and Aliha [25] proposed a diagonally loaded square plate containing an inclined center crack for investigating mixed mode fracture behavior. In the above-mentioned studies, brittle fracture experiments have been conducted either on PMMA or other brittle or quasi-brittle materials like ceramics and rocks. However, some of these specimens have certain shortcomings. For example, some of the mixed mode test configurations are able to provide only limited mode mixities or require complicated loading fixtures.

The specimens of circular or semi-circular shape are very suitable for fracture testing on rock or asphalt materials because they can be easily cut from cylindrical cores which are traditionally prepared from such materials. However, as elaborated in the next section, the classical SCB specimen has certain shortcomings for mixed mode fracture experiments. Therefore, a modified SCB test specimen is proposed in this paper to overcome the previous weaknesses. In the forthcoming sections, the suggested specimen is described and then its capabilities and advantages are investigated by means of finite element analysis and also through some fracture tests conducted on PMMA.