Research On Dynamic Properties Of Samples With Cracks

What this paper study on is based on research of Type I size effect by professor Qi. Professor Qi did theoretical research about complete sample under dynamic load （Type I size effect） and obtained theoretical formula among strength of sample, size and strain rate. Physical mechanism is revealed successfully. At the same time, theoretical formula of average fracture size of sample, critical strain rate of static and dynamic size effect. According to the study of professor Qi, we may infer that there should be connection which is similar to Type I size effect between static and dynamic size effect of Type II size effect. Therefore, main research of this paper is relation between strength and strain rate of Type II size effect, namely, cracked or notch samples.The main contents and achievements are as follows:Theoretical formula of dynamic intensity factor and strain rate when samples with Mode I crack under linear load is obtained by theoretical deduction and using basic theory of dynamic fracture mechanics. Considering boundary conditions, initial conditions and influence of inertia effect, a set of dual equations is obtained and these equations are solved using Wiener-Hopf method. Theoretical formula of dynamic intensity factor and strain rate is finally obtained using Laplace transform. From the result two conclusions is got,1)There is linear relation between dynamic intensity factor and strain rate for cracked samples, which is similar to test result of Hong and Li[13]. This indicates there is similar relationships between complete samples and cracked samples, which verified the inference before.2)Considering σ₀t= σ and 3/2 power relationship between dynamic intensity and time t, equation （3-50） can be rewritten as ,i.e. K_1d～t^-1/2. This result is similar to dynamic intensity of sudden load, which can verify correctness of the equation.Considering the equation between dynamic strength of sample and size, strain rate deduced by Maxwell model and interaction before Rayleigh wave reaches the other crack tip, the equation of minimum critical crack size is deduced. Compared two conditions, the former offers stronger restriction, so the result got from former condition is more accurate. Then four conclusions are got,1)The Maxwell model offers more restriction, so to plane crack and coin-like crack, equation （4-11） and equation （4-18） are more acceptable.2)The relationship between minimum critical crack size and strain rate is a～ε^-2/3, which is similar to Grady’s theoretical conclusion[10] and experimental results of Gilvarry and Bergstrom[11], which verified correctness of equation.3)There is similar relationship between plane crack and coin-like crack. However, the minimum critical size of coin-like crack is bigger than that of plane crack, which is due to that coin-like crack is limited by surrounding structure and more power is needed for startup of crack.4)The minimum critical size decrease as strain rate increase, which illustrates higher strain rate activates smaller crack. This indicates that more energy is needed to activate smaller crack. In other words, when a solid with an array of cracks is loaded statically, the largest crack will dominate the response of the solid, limiting the maximum load that can be applied. In the dynamic case, however, the largest crack no longer dominates; rather, cracks with a wide range of sizes are clearly activated simultaneously. So, the failure occurs by fracturing the solid through multiple crack growth.3.Qualitative relation between static strength and dynamic strength is obtained using energy method, which offers reference and basis for determining the relationship between static strength and dynamic strength of Type Ⅱ size effect.