Shigeo Takezono

Fatigue crack propagation under step variation of stress frequency in orthotropic material

Abstract The effect of variation of stress frequency on fatigue crack propagation in 99.5% pure titanium, which has remarkable strain rate dependence in the plastic region and anisotropy, was studied. Fatigue crack propagation tests were carried out under four stress frequencies: two constant stress frequencies ( f = 20 Hz , 0.02 Hz ) and two stress frequencies changed step-wise ( f = 20→ 0.02 Hz , 0.02 → 20 Hz ). The test specimens were cut out from rolling direction and transverse direction to rolling of the plate. An orthotropic elasto/visco-plastic analysis of fatigue crack propagation was performed by the use of the orthotropic visco-plastic model, and the comparison between the change of crack propagation rate due to variation of stress frequencies and the visco-plastic strain behavior at the crack tip calculated by the analysis was made. The results obtained in this study are summarized as follows: 1. (1) It was found from the experiments that the crack propagation rate changed characteristically depending on cutting out direction of the specimen caused by anisotropy of titanium plate and on the variation of stress frequency. 2. (2) A parameter closely related to the fatigue crack propagation rate is the visco-plastic strain range at the crack tip. 3. (3) The effect of variation of stress frequency on the fatigue crack propagation rate may be explained by the variation of the visco-plastic strain range at the crack tip based on an anisotropic visco-plasticity of the materials.

The Mechanical Behavior Analysis of CFCC with Overall Anisotropic Damage by the Micro-Macro Scale Method

In this paper, a micro-macromechanical approach is used to establish the macroscopic constitutive model with anisotropic damage in continuous fiber reinforced ceramic matrix composites (CFCC). For microlevel analysis of unit cell, the homogenization method based on double-scale asymptotic expansion is used to derive the material properties of composites. The macrolevel analysis is conducted to compute the macrostresses and strains with anisotropic damage. The two analyses are conducted by using Finite Element Method (FEM). An overall anisotropic damage tensor for the whole composite is used to describe all types of damage that composite undergoes, such as matrix cracking, fiber breakage, and interfacial damage between matrix and fiber. The damage evolution equation is obtained by using thermodynamic theory. The numerical calculation is carried out to investigate and to predict the onset and evolution of anisotropic damage for composites with different types of laminate. The damage material parameters are determined by fitting the numerical results to the experimental data, and some results are compared well with experimental results in the literature [Wang, S.W. and Parvizi-Majidi, A. (1992). Experimental Characterization of the Tensile Behavior of Nicalon Fiber-Reinforced Calcium Aluminosilicate Composites, Journal of Materials Science, 27: 5483-5496.]. By using the proposed model, the stiffness and nonlinear stress-strain response of brittle composite materials are predicted, and the macroscopic elastic brittle anisotropic damage behavior is also described

Application of fracture mechanics to the surface crack propagation in stainless steel at elevated temperatures

Abstract The propagation of small surface cracks in SUS 304 stainless steel is examined at elevated temperatures. In the temperature region studied, the crack growth is mainly cycle-dependent. When temperature is higher than 500°C, creep-dependent crack growth becomes dominant which results in a larger crack growth rate. By confirming that the surface crack maintains a semi-elliptic shape during its growth and by investigating the cyclic deformation behavior of the material, elastic-plastic fracture mechanics parameters are evaluated and used to correlate the crack growth rate. Both the J integral range ΔJ, and the effective J integral range ΔJeff, which accounts for the crack closure effect, are found to be excellent to consolidate crack growth rates for the high temperature fatigue conditions.

The dislocation-free zone at a mode I crack tip

Abstract The distribution of dislocations in the vicinity of a mode I crack tip is formulated based on the observation of a single crystal specimen of aluminium by transmission electron microscopy (TEM). Closed form expressions of the dislocation density function and the dislocation-free zone (DFZ) condition for a mode I crack are derived. The relationship between the size of the crack, dislocation-free zone and plastic zone is obtained as a function of the applied stress. The characteristic of this model is compared with that of the model proposed by Chang and Ohr for a mode III crack.

Nonlocal elastic damage near crack tip

A constitutive modeling for nonlocal elastic damage near crack tip is proposed. A calculation method for nonlocal elastic damage is introduced and the computational results for stress and damage are given by means of finite element method.

Effect of loading frequency on fatigue crack growth under high temperature

Abstract The effect of loading frequency on the fatigue crack growth under high temperature is studied. The high temperature fatigue crack growth tests for pure titanium (99.5%) are carried out under three loading frequencies (2, 6, 20 Hz). An elasto/viscoplastic constitutive equation which fully couples strain to continuum damage is used to analyse fatigue crack growth at high temperature. A damage criterion is employed for predicting the crack growth which is related to the actual material failure ahead of the crack tip. By means of FEM, the mechanical fields ( σ ij , e ij , D ) and the dependence of crack growth rate on loading frequency and viscoplastic strain at the crack tip are investigated in detail. The numerical simulation results of the fatigue crack growth are shown and compared with the experimental ones. The results in the present study show that: (1) the stress at the crack tip element decreases rapidly with the cyclic numbers. There is no stable state of stress distribution in the fatigue process when material damage is taken into account. (2) The crack tip stress is lower than the peak stress and the peak stress takes place at a location away from the crack tip. No stress singularity is present at the crack tip. (3) The fatigue growth rate dl/dN is closely related to the Δe y vp obtained by numerical analysis. If d t /d N is plotted against Δ e y vp , the relation can be expressed by a straight line in logarithmic coordinates for any loading frequency.

Propagation of small surface cracks in stainless steel at high temperature

Abstract Growth behavior of small surface cracks in stainless steel is experimentally examined at 500°C and room temperature. The crack is confirmed to maintain a semi-elliptic shape during its growth. Cyclic deformation behavior of the material is investigated to evaluate elasto-plastic fracture mechanics parameters. It is found that crack growth rates have a good correlation with the strain intensity factor range ΔK e and J -integral range ΔJ .

A nonlocal damage mechanics approach to high temperature fatigue crack growth

Abstract A nonlocal damage constitutive model is developed for elasto/visco-plastic materials and is used to analyze fatigue crack growth at high temperature. In this model, no kinematic hardening rule is needed to account for the subsequent yielding and strain hardening behavior of the materials. A calculation method for nonlocal damage is introduced. The fatigue crack growth tests at high temperature for pure titanium (99.5%) are carried out. By means of FEM, the mechanical fields (σij, ϵij, D) and their redistribution due to damage effect near the crack tip are investigated. The numerical simulation results of the fatigue crack growth are shown. The validity of the presented damage model is verified by comparing the FEM numerical simulation with experimental results.

A nonlocal damage approach to analysis of the fracture process zone

Abstract A two-zone fracture process model with a crack-bridging zone (CBZ) and a microcracking zone (MCZ) is proposed to describe the fracture process around the tip of a macrocrack. A nonlocal damage approach based on previous work is used to determine the size of the fracture process zone (FPZ). The experimental analysis given by Horii and Ichinomiya [Int.J. Fracture51, 19–29 (1991)] supports the proposal that the existence of the crack bridging effect brings out an increase in load-carrying capacity of materials, whereas microcracking leads to the deterioration of the capacity. Based on the above and utilizing Westergaards complex function, the distribution functions of stress arid damage in the FPZ are given. Applying these to the concrete-like material mortar, we can determine the distribution functions of stress and damage in the FPZ if load and crack opening displacement (COD) at a point are given. Additionally, a nonlocal damage failure criterion is proposed to judge the propagation of the macrocrack.

Dependence of stress frequency on fatigue crack initiation in orthotropic material

Abstract The effect of stress frequency on fatigue crack initiation in 99.5% pure titanium plate, which has remarkable strain rate dependence in the plastic region and notable orthotropy, was studied. Fatigue crack initiation tests were carried out under three kinds of stress frequencies (0.2, 1 and 20 Hz). The test specimens were cut out from the rolling direction and the transverse to rolling direction of the plate. An anisotropic elasto/visco-plastic analysis was performed by the use of the orthotropic elasto/visco-plastic overlay model, and the comparison between the cycles to crack initiation and the visco-plastic strain range at notch root obtained by the analysis was made. The results obtained in this study are summarized as follows: 1. (1) It was found from the experiment that the cycles to fatigue crack initiation depended on the cutting out direction of the specimen because of the anisotropy of titanium plate, and were approximately in proportion to f n (n > 0) , where f is the stress frequency. 2. (2) A parameter closely related to the fatigue crack initiation in orthotropic material is the visco-plastic strain range strain range at the notch root, and the cycles to fatigue crack initiation is approximately in inverse proportion to the nth power of the visco-plastic strain range at the notch root. 3. (3) The effect of stress frequency on fatigue crack initiation may be explained by the variation of visco-plastic strain range at notch root based on the strain rate dependence and the anisotropy of the material.