13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Stress Concentration based on Non-linear Motion Equations and its Application for Non-destructive Detection of Plate Jianhua Xiao1,*, Jingjing Wang1 1 Measurement Institute, Henan Polytechnic University, Jiaozuo 454000, China * Corresponding author: jhxiao@hpu.edu.cn Abstract For a plate with large deformation, where the possible fracture will be initiated is an important problem. It is true that the defects or voids of material usually are the initial positions. However, the more important problem is the local defect (fatigue-fracture) caused by the global deformation of medium, as this problem is very common in practical engineering. For this purpose, two sets of non-linear motion equations of deformation established in rational mechanics frame are used to study this problem. The stress concentration problem is defined as: for a given deformation, how the stresses are distributed to meet the motion equations under the cost of fatigue-fracture within the plate. The motion equations show that the local curvature is the main cause of fatigue-fracture. Taking the local deformation curvature as a parameter function, the stress transportation solution is obtained. The result shows that: for plate bending, the stress is varied in exponential law with the path-integral of local curvature of plate. In non-destructive detect, when the pressure wave data are recorded in an array, they can be used to inverse the intrinsic local curvature of target medium region. Then, the “inversed” local curvature can be used to predict the potential fatigue-cracking initiation region. Keywords Nondestructive detect, Stress concentration, Stress transportation, Non-linear motion equation, Large deformation 1. Introduction Stress concentration usually is addressed by the irregular boundary problems [1-3]. As a simple example, for a plate with small hole, the stress around hole will be increased rapidly when the in-plane stretching is increased. To express the effects of stress concentration, a factor (defined as maximum stress over name stress) is introduced. Its shortage is that the voids geometry features are required. Then, taking the voids as boundary, the motion equations are used to calculate the factor based on theoretic solutions. The crack tip field theory is fully developed along this theoretic line. Hence, it is understandable that many researchers focus on their attention upon micro-scale phenomena. However, based on experiences, we usually have no ad-hoc information about where the defects exist. What we want to know is where the fatigue-fracture will be initiated? The micro-scale structure description has little help on this topic. Generally, for uniform continuum, the stress concentration phenomena can be attributed to the cause of the defects of micro-scale structures. For a plate with arbitral deformation, the real fatigue-fracture frequently appears in the highest curvature position or the position inherited with large scale deformation or singularity. On phenomenon sense, the defects or voids of material were produced by the macro deformation in space-time domain. Recently, how the macro deformation alters the microstructures of material is raised as an important problem for fracture mechanics. The dual scale or multiscale viewpoint is proposed to answer how the macro deformation causes the microstructure instability [4-6]. To answer this question, the first problem is returned to the question about where the stress will be concentrated. This problem may be answered by formulating related motion equations. For this purpose, two sets of non-linear motion equations of deformation [7] established in rational
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