Loading rate effects on parameters of the Weibull stress model for ferritic steels

This study investigates the effects of loading rate on parameters of the Weibull stress model for prediction of cleavage fracture in a low strength, strongly rate-sensitive A515-70 pressure vessel steel. Based on measured, dynamic fracture toughness data from deep- and shallow-cracked SE(B) specimens, the calibrated Weibull modulus (m) at shows little difference from the value calibrated previously using static toughness data. This newly obtained result supports the hypothesis in an earlier study [Gao X, Dodds RH, Tregoning RL, Joyce JA. Weibull stress model for cleavage fracture under high-rate loading. Fatigue Fract Engng Mater Struct 2001;24:551-64] that the Weibull modulus likely remains rate independent for this material over the range of low-to-moderate loading rates. Additional experimental and computational results for higher rates show that a constant m-value remains applicable up to the maximum loading rate imposed in the testing program . Rate dependencies of the scale parameter (σ_u) and the threshold parameter (σ_w-min) are computed using the calibrated m, and the results indicate that σ_u decreases and σ_w-min increases with higher loading rates. The predicted cumulative probability for cleavage fracture exhibits a strong sensitivity to small changes in σ_u. Consequently, σ_u must be calibrated using dynamic fracture toughness data at each loading rate of interest in an application or selected to make the Weibull stress model predict a dynamic master curve of macroscopic toughness for the material.     

Effect of adhesive thickness on fatigue and fracture of toughened epoxy joints – Part I: Experiments

The effect of bondline thickness, from 130 μm to 790 μm, on the fatigue and quasi-static fracture behavior of aluminum joints bonded using a toughened epoxy adhesive was studied experimentally under mode-I (DCB) and mixed-mode (ADCB) loading. Under mode-I loading, it was found that the fatigue threshold energy release rate, G_th, decreased for very thin bondlines, while under mixed-mode loading, the G_th changed very little with bondline thickness. In both cases, the effect of bondline thickness was more pronounced at higher crack growth rates. For quasi-static fracture, the effect of adhesive thickness on the energy release rate for the onset of fracture from the fatigue threshold, G_c0, was similar to that found for the fatigue threshold; however, the steady-state energy release rate, , increased linearly with increasing bondline thickness.     

Determining double-K fracture parameters of concrete for compact tension and wedge splitting tests using weight function

The paper presents use of universal form of weight functions for determining the double-K fracture parameters and on compact test and wedge splitting test specimens. The proposed method enables to obtain a closed form expression of cohesion toughness of concrete specimens. A comparison with existing analytical method shows that the weight function method for determination of double-K fracture parameters yields results without any appreciable error. Significant influence of initial notch to depth (a₀/D) ratio on the double-K fracture parameters is not also observed. Finally, a possible definition of brittleness of concrete using double-K fracture parameters is proposed.     

Three-dimensional effects on fatigue crack closure under fully-reversed loading

For extension of fatigue cracks at engineering length-scales, the increase in crack opening loads (K_op) caused by plasticity-induced closure plays a key role in estimates of growth rates in structural metals. Under conditions of small-scale yielding, our prior work reveals the existence of a similarity scaling parameter, , that scales the effects of differing peak load (K_max), specimen thickness (B), and material yield stress (σ₀) on K_op/K_max across varying materials and loading levels. This work explores the applicability of the scaling parameter to specimens under fully-reversed (i.e. R = −1) cyclic fatigue loading. Numerical results again show that the magnitude of K_op/K_max at each location along the crack front remains unchanged when K_max, thickness, and material yield stress all vary to maintain a fixed value of .     

Evaluation of dynamic fracture toughness KId by Hopkinson pressure bar loaded instrumented Charpy impact test

A novel method for measuring the dynamic fracture toughness, K_Id, using a Hopkinson pressure bar loaded instrumented Charpy impact test is presented in this paper. The stress intensity factor dynamic response curve (K_I(t)−t) for a fatigue-precracked Charpy specimen is evaluated by means of an approximate formula. The onset time of crack initiation is experimentally detected using the strain gauge method. The value of K_Id is determined from the critical dynamic stress intensity factor at crack initiation. A K_Id value for a high-strength steel is obtained using this method at a stress-intensity-factor rate () greater than 10⁶ MPa .     

Electrohydrodynamic pulsatile flow in a channel bounded by porous layer of smart material

Electrohydrodynamic dispersion due to pulsatile flow in a channel bounded by porous layer of smart material is studied considering both steady and unsteady cases using both BJ and BJR-slip conditions. We found that in the case of steady flow, the dispersion coefficient, decreases with an increase in electric number W_e but increases with an increase in porous parameter σ_p in the case of BJ-slip condition. However this nature is different in the case of BJR-slip condition in the sense that the dispersion coefficient, increases for certain values of W_e and then decreases with an increase in W_e. In the case of unsteady flow, the dispersion coefficient, , decreases with an increase in W_e and σ_p for both BJ and BJR conditions. In particular, we found that the value of for steady flow in the case of BJ-slip condition is less than that of unsteady flow. The opposite is true for BJR condition. The findings are useful in the design of robust and efficient artificial organs in the human body.     

Theoretical analysis of the effects of relative crack length and loading angle on the experimental results for cracked Brazilian disk testing

Based on the closed-form expressions of the stress intensity factors for a central cracked circular disk, four error transfer functions of the stress intensity factors were introduced in order to analyze the effect of the relative crack length and the error of loading angle on the experimental results for Brazilian disk testing. The analyzed results show that the precision of are relevant on the relative crack length and the error of loading angle. Further analysis show that the error of loading angle Δθ has a significant effect on the errors of under mixed-mode loading condition, but Δθ has nearly no effect on the error of K_I under pure mode I loading condition and smaller effect on that of K_II under pure mode II loading condition. Finally, the recommended range of the relative crack length is between 0.4 and 0.6.     

Fracture behavior under mixed-mode loading of ceramic plasma-sprayed thermal barrier coatings at ambient and elevated temperatures

The fracture behavior under modes I and II loading of ceramic plasma-sprayed thermal barrier coatings was determined in air at 25 and 1316 °C in asymmetric four-point flexure. The mode I fracture toughness was found to be K_Ic = 1.15 ± 0.07 and 0.98 ± 0.13 MPa , respectively, at 25 and 1316 °C. The respective ‘nominal’ mode II fracture toughness values were K_IIc = 0.73 ± 0.10 and 0.65 ± 0.04 MPa . The empirical mixed-mode fracture criterion best described the coatings’ fracture behavior under mixed-mode loading. The angle of crack propagation was in reasonable agreement with the minimum strain energy density criterion.     

Temperature dependence of Weibull stress parameters: Studies using the Euro-material

This work demonstrates the temperature invariance of the Weibull stress modulus, m, for a 22Ni-MoCr37 pressure vessel steel through calibrations at two extreme temperatures of the ductile-to-brittle transition. This temperature invariance reflects the characterization of microcrack size distribution in the material described by the modulus. The calibrations performed here also demonstrate the clear dependence of the Weibull scale parameter, σ_u, on temperature. The increase of σ_u with temperature reflects the increase in microscale toughness of ferritic steels. The calibration procedure employs a three-parameter Weibull stress model which includes the effects of a minimum (threshold) toughness, K_min. The calibrations suggest that K_min increases gradually with temperature. Finally, an engineering procedure is presented to enable practical applications of the Weibull stress model for defect assessments. This procedure combines the demonstrated temperature invariance of m, a recently developed method for predicting the variation of σ_u with temperature using the Master Curve, and calibration of the Weibull stress parameters at one temperature. The (calibrated) temperature invariant m and the estimated σ_u as a function of temperature are used to predict the cumulative probability of fracture for several large datasets without direct calibration.     

Determination of fracture parameters for crack propagation in concrete using an energy approach

Double-G fracture model, a new analytical model describing fracture behaviour on cracked concrete, was recently proposed by Xu and Zhao based on the conception of energy release rate. This model couples the Griffith brittle fracture theory with the bridging softening property of concrete, and it is an extension of double-K fracture model proposed by Xu and Reinhardt. In this model, two fracture parameters, i.e., the initiation fracture energy release and the unstable fracture energy release , are termed to distinguish the different crack propagation stages undergoing during the whole fracture process in concrete. The difference between the two parameters, written as , is assumed to come from the contribution by aggregate bridging interlock, which results in the presence of fracture process zone. In our present work, firstly, the new model is elaborately introduced. Then, fracture tests are conducted, where besides three-point bending beams, a new testing method, called wedge-splitting on compact tension is adopted. In the experiments, electrical strain gauges are used to measure initial cracking load. Based on recorded load-crack mouth opening displacement curve (P-CMOD) or load-displacement curve (P-δ) and load-strain curve (P-ε), double-G fracture parameters are experimentally determined. Further more, based on the assumed three parameters relationship among , and , unstable fracture energy release are calculated. A comparable result between the measured and the calculated confirms this assumption. In order to verify the feasibility of this new model, the effective double-K fracture parameters converted by double-G fracture parameters using are compared with the double-K fracture parameters calculated by double-K fracture model. It is found that there is a good agreement. Another two series of different initial crack-depth ratios three-point bending beams carried out by Refai and Swartz are also collected to provide more experimental verification. It shows that the results obtained from the double-G fracture model agree well with those of double-K fracture model.     

An analytical model to predict the effective fracture toughness of concrete for three-point bending notched beams

An analytical model to predict the effective fracture toughness of concrete was proposed based on the fictitious crack model. Firstly, the equilibrium equations of forces in the section were formed in combination with the plane section assumption. Then a Lagrange function was presented through the equilibrium equations and the relationship formula between the effective crack length and crack tip opening displacement. Taking into account Lagrange Multiplier Method, the maximum load P_max was obtained, as well as the critical effective crack length a_c. Furthermore, was gained in an analytical manner. Subsequently, some material and structural parameters from other literatures were adopted into the proposed model for the calculation. Compared with the experimental results, most of the calculated values show a good agreement for P_max and a_c. In order to study the influence of the softening curve in the fictitious crack on the calculated fracture parameters, three series of constants determining the shape of the softening curve were chosen in the calculation. The results show that the calculated fracture parameters are not sensitive to the shape of the softening curve. Therefore, only if the elastic modulus E_c and flexural tensile strength f_r were measured, P_max, a_c and can be predicted accurately using the proposed model. Finally, the variations of the calculated fracture parameters with the specimen size and a₀/h (i.e., the ratio of the initial crack length to the depth of the specimen) were studied. It was found that both and the pre-critical crack propagation length Δa_c increase with the specimen size. However, the two parameters increase to the maximums and then decrease gradually with a₀/h. Moreover, the theories of free surface effect were utilized to explain the observed size effects.     

Symbolic computation and construction of soliton-like solutions to the (2 + 1)-dimensional dispersive long-wave equations

By means of a new Riccati equation expansion method, we consider the (2 + 1)-dimensional dispersive long-wave equations , η_t+(uη+u+u_xy)_x=0. As a result, we not only can successfully recover the previously known formal solutions obtained by known tanh function methods but also construct new and more general formal solutions. The solutions obtained include the nontravelling wave and coefficient functions’ soliton-like solutions, singular soliton-like solutions, triangular functions solutions.