Numerical simulation study on shear resistance of anchorage joints considering tensile-shear fracture criterion of 2G-NPR bolt

2G-NPR bolt (the 2nd generation Negative Poisson’s Ratio bolt) is a new type of bolt with high strength, high toughness and no yield platform. It has signifcant efects on improving the shear strength of jointed rock mass and controlling the stability of surrounding rock. To achieve an accurate simulation of bolted joint shear tests, we have studied a numerical simulation method that takes into account the 2G-NPR bolt's tensile–shear fracture criterion. Firstly, the indoor experimental study on the tensile–shear mechanical properties of 2G-NPR bolt is carried out to explore its mechanical properties under diferent tensile–shear angles, and the fracture criterion of 2G-NPR bolt considering the tensile–shear angle is established. Then, a three-dimensional numerical simulation method considering the tensile–shear mechanical constitutive and fracture criterion of 2G-NPR bolt, the elastoplastic mechanical behavior of surrounding rock and the damage and deterioration of grouting body is proposed. The feasibility and accuracy of the method are verifed by comparing with the indoor shear test results of 2G-NPR bolt anchorage joints. Finally, based on the numerical simulation results, the deformation and stress of the bolt, the distribution of the plastic zone of the rock mass, the stress distribution and the damage of the grouting body are analyzed in detail. The research results can provide a good reference value for the practical engineering application and shear mechanical performance analysis of 2G-NPR bolt.

Evaluation of varying ductile fracture criterion for 7075 aluminum alloy

As one of the principal failures,ductile fracturing restricts metal forming process.Cockcroft-Latham type fracture criterion is suited for ductile fracture in bulk metal-forming simulation.Finding a way to evaluate the ductile fracture criterion（DFC） and identify the relationship between DFC and deformation conditions for a strain-softening material,7075 aluminum alloy;however,it is a non-trivial issue that still needs to be addressed in a greater depth.An innovative approach is brought forth that the compression tests and numerical simulations provide mutual support to evaluate the ductile damage cumulating process and determine the DFC diagram.One of the results shows that for a fixed temperature,the maximum cumulated damage decreases regularly with increasing strain rate.The most important result shows that DFC of 7075 aluminum alloy at temperatures of 573-723 K and strain rates of 0.01-10 s-1 is not a constant but a change in a range of 0.255-0.453,thus it has been defined with varying ductile fracture criterion（VDFC） and characterized by a function of strain rate and temperature.According to VDFC diagram,the exact fracture moment and position during various forming processes will be predicted conveniently,in addition to which,the deformation domains with lower fracture risk corresponding to higher VDFC can be identified.

A New Ductile Fracture Criterion and Its Application to the Prediction of Forming Limit in Deep Drawing

With considering the influence of equivalent plastic strain on void-damage and taking Lemaitre damage equivalent stress as plastic potential, based on continuous damage mechanics theory, a new criterion for ductile fracture is derived. The two key material constants in the criterion are determined by the combination of tension tests with FE (finite element) simulation. On the basis of the values of stress and strain calculated from commercial finite element software, the forming limit in cylindrical deep drawing of annealed aluminum alloy LY12(M) is predicted by means of the new ductile fracture criterion. Experiments verify that the predicted results are in agreement with the experimental ones. Hence, it is reliable to predict the forming limit in deep drawing by means of the new ductile fracture criterion.

Fracture strength evaluation of titanium alloys using modified average stress criterion

Structural integrity procedures were used to demonstrate the fitness for the purpose of engineering components transmitting loads. The prediction of the fracture strength of titanium alloys containing sharp notches through the damage model depends on the un-notched strength and the critical length of the damage zone ahead of the notch. In general, the critical length of the damage zone depends on the material, specimen, and size of the sharp notch. Modifications were made in one of the stress fracture criteria known as the average stress criterion for accurate prediction of notched tensile strength of titanium alloy specimen containing sharp notches. To examine the adequacy of these modifications, fracture data of center-cracked titanium alloys with various thicknesses are considered. The notched （fracture） strength estimates are found to be close to the test results. The modified average stress criterion is very simple to predict the notched tensile strength.

A DUCTILE FRACTURE CRITERION BASED ON THREEDIMENSIONAL VOID MODEL

A fracture criterion derived from a microscopic point of view is proposed and has proved to be effective in the analysis of uniaxial tension. On the one hand, a method of predicting a ductile fracture is proposed using a three-dimensional void model and the assumption of velocity discontinuity. The relationship between the void volume fraction and the critical strain to fracture, calculated with the help of the new model, shows the same tendency as that obtained from the modified Thomason model. On the other hand, the mechanical and metallographic analyses of the uniaxial tension experiment are performed using four kinds of carbon steel. The relationship between the void volume fraction and the critical strain to fracture, calculated from the new model, agrees better with the result obtained from the experiment, rather than that calculated by the modified Thomason model, which confirms the validity of the ductile fracture criterion based on the three-dimensional void model.

SIF-based fracture criterion for interface cracks

The complex stress intensity factor K governing the stress field of an interface crack tip may be split into two parts, i.e.,■ and s^（-iε）, so that K = ■ s^（-iε）, s is a characteristic length and ε is the oscillatory index. ■ has the same dimension as the classical stress intensity factor and characterizes the interface crack tip field. That means a criterion for interface cracks may be formulated directly with■, as Irwin（ASME J. Appl. Mech. 24：361–364, 1957） did in 1957 for the classical fracture mechanics. Then, for an interface crack,it is demonstrated that the quasi Mode I and Mode II tip fields can be defined and distinguished from the coupled mode tip fields. Built upon SIF-based fracture criteria for quasi Mode I and Mode II, the stress intensity factor（SIF）-based fracture criterion for mixed mode interface cracks is proposed and validated against existing experimental results.

Thermo-hydro-mechanical-chemical(THMC)coupling fracture criterion of brittle rock

Based on analysis of thermo-hydro-mechanical-chemical(THMC)coupling mechanism for brittle rock,THMC coupling indicator in terms of rock porosity was introduced to represent the influencing degree of THMC coupling field on stress field in order to establish THMC coupling fracture criterion.A novel real-time measurement method of permeability(related to porosity)was proposed to determine the THMC coupling indicator,and self-designed THMC coupling tests and scanning electron microscope tests were conducted on pre-cracked red sandstone specimens to study the macroscopic and microscopic fracture mechanism.Research results show that the higher the hydraulic pressure is,the smaller the crack initiation load is and the easier the Mode I fracture occurs.Test results are in good agreement with prediction results(crack initiation load and angle,and fracture mode),which can verify the effectiveness of the newly established THMC coupling fracture criterion.This new fracture criterion can be also further extended to predict THMC coupling fracture of multi-crack problem.

Fracture criterion for predicting surface cracking of Ti40 alloy in hot forming processes

Hot compression tests were conducted on Ti40 burn resistant titanium alloy in the temperature range of 900-1 100 ℃ and strain rate range of 0.01-10 s-1 to investigate its fracture behavior and critical fracture conditions in hot forming. It was observed that the failure of Ti40 alloy is attributed to longitudinal surface cracking due to severe oxidation of element V and the secondary tensile stresses. The critical fracture strain increases with increasing temperature and decreasing strain rate. From these observations and parallel FEM simulations,it was concluded that the critical fracture strain is a function of a single argument Zener-Hollomon parameter,and there is a linear relationship between them. An Oyane criterion successfully predicted the location of crack initiation. The critical fracture values also exhibit a liner relationship with lnZ. Based on these results,a new fracture criterion of Ti40 alloy based on Zener-Hollomon parameter was established.

The Fatigue Fracture Criterion Based on the Latent Energy Approach

The extensive literature on the fatigue problem, published for more than one hundred years, is reviewed by the known scientists [1,2]. As it follows from these investigations, the fundamental amount of failures in engineering practice connected with the fatigue fractures of materials and structure elements. The fatigue problem is complicated one and it is not solved yet. So the theoretical and experimental investigations of this problem will be continued. In our paper the energy approach to formulate the fatigue strength criterion is proposed. The criterion is based on the conception of the latent energy [3-7]. This conception was not applied previously to the fatigue problem. The latent energy is consumed to generate the irreversible deformation and to damage and fracture of metallic materials. So the fatigue fracture criterion can be formulated using the results of latent energy measurements in the macro experiments. This is most impotent advantage of the proposed approach. The logistic function is used to describe the dependence of latent energy from the value of irreversible deformation. It is assumed that the cyclic strength of metals is defined by the latent energy, stored in specimen, when it is reached the critical value in accordance with the logistic curve in a saturation zone. This proposal is used to formulate the fatigue strength criterion. The functions and parameters of received criterion are concretized and comparisons with experimental results for axial cyclic tension for sheet aluminum alloy specimens are given.

Two Modes and Criterion of Brittle Fracture

The plastic zone at the tip of the flaw (including acute cark and common notch) was investigated. Forthe notch specimen, a formula of toughness K was proposed, and its physical meaning was emphasized.Twomodes of brittle fracture was identified and the evaluating criterion was established.

Evaluation of Energy Saving Operational Modes for Industrial Fracture Connected Processes on the Basis of Incubation Time Fracture Criterion

A problem for a central crack in a plate subjected to plane strain conditions is investigated. Mode I crack loading is created by a dynamic pressure pulse applied at a large distance from the crack. It was found that for a certain combination of amplitude and duration of the pulse applied, the energy transmitted to the sample has a strongly marked minimum, meaning that with the pulse amplitude or duration moving away from the optimal values, minimum energy required for initiation of crack growth increases rapidly. The results obtained indicate a possibility to optimise energy consumption of different industrial processes connected with fracture. Much could be gained in, for example, drilling or rock pounding where energy input accounts for the largest part of the process cost. Presumably further investigation of the effect observed can make it possible to predict optimal energy saving parameters, i.e. frequency and amplitude of impacts, for industrial devices, e.g. bores, grinding machines, and hence significantly reduce the process cost. The pre- diction can be given based on the parameters of the media fractured （material parameters, prevalent crack length and orientation, etc.）.

A New Fracture Criterion for a Crack under Combined Mode Loading

A new fracture criterion was proposed. The physical explanation of the criterion is that crack will propagate when the minimum strain energy density in iso hoop stress curve reach a critical strength of the material considered. The resulting curve of critical fracture of mixed mode cracks shows that the present fracture is efficient and more accurate than the previous criteria.

Maximum twin shear stress factor criterion for sliding mode fracture initiation

Previous researches on the mixed mode fracture initiation criteria were mostly focused on opening mode fracture. In this study, the authors proposed a new criterion for mixed mode sliding fracture initiation, which is the maximum twin shear stress factor criterion. The authors studied a finite width plate with central slant crack, subject to a far field uniform uniaxial tensile or compressive stress.

Prediction and Control of Wrinkle and Fracture for Stamping Regular Polygonal Box

Based on the deformation characteristic of regular polygonal box stamped parts and the superfluous triangle material wrinkle model,the criterion of regular polygonal box stamped parts without wrinkle was deduced and used to predict and control the wrinkle limit.According to the fracture model,the criterion of regular polygonal box stamped parts without fracture was deduced and used to predict and control the fracture limit.Combining the criterion for stamping without wrinkle with that without fracture,the stamping criterion of regular polygonal box stamped parts was obtained to predict and control the stamping limit.Taken the stainless steel0Cr18Ni9(SUS304)sheet and the square box stamped part as examples,the limit diagram was given to predict and control the wrinkle,fracture and stamping limits.It is suitable for the deep drawing without flange,the deep drawing and stretching combined forming with flange and the rigid punch stretching of plane blank.The limit deep-drawing coefficient and the minimum deep-drawing coefficient can be determined,and the appropriate BHF(blank holder force)and the deep-drawing force can be chosen.These provide a reference for the technology planning,the die and mold design and the equipment determination,and a new criterion evaluating sheet stamping formability,which predicts and controls the stamping process,can be applied to the deep drawing under constant or variable BHF conditions.

Comparison of Modified Mohr-Coulomb Model and Bai-Wierzbicki Model for Constructing 3D Ductile Fracture Envelope of AA6063

Ductile fracture of metal often occurs in the plastic forming process of parts.The establishment of ductile fracture criterion can effectively guide the selection of process parameters and avoid ductile fracture of parts during machining.The 3D ductile fracture envelope of AA6063-T6 was developed to predict and prevent its fracture.Smooth round bar tension tests were performed to characterize the flow stress,and a series of experiments were conducted to characterize the ductile fracture firstly,such as notched round bar tension tests,compression tests and torsion tests.These tests cover a wide range of stress triaxiality(ST)and Lode parameter(LP)to calibrate the ductile fracture criterion.Plasticity modeling was performed,and the predicted results were compared with corresponding experimental data to verify the plasticity model after these experiments.Then the relationship between ductile fracture strain and ST with LP was constructed using the modified Mohr-Coulomb(MMC)model and Bai-Wierzbicki(BW)model to develop the 3D ductile fracture envelope.Finally,two ductile damage models were proposed based on the 3D fracture envelope of AA6063.Through the comparison of the two models,it was found that BW model had better fitting effect,and the sum of squares of residual error of BW model was 0.9901.The two models had relatively large errors in predicting the fracture strain of SRB tensile test and torsion test,but both of the predicting error of both two models were within the acceptable range of 15%.In the process of finite element simulation,the evolution process of ductile fracture can be well simulated by the two models.However,BW model can predict the location of fracture more accurately than MMC model.

Mechanical Properties,Damage and Fracture Mechanisms of Bulk Metallic Glass Materials

The deformation, damage, fracture, plasticity and melting phenomenon induced by shear fracture were investigated and summarized for Zr-, Cu-, Ti- and Mg-based bulk metallic glasses （BMGs） and their composites. The shear fracture angles of these BMG materials often display obvious differences under compression and tension, and follow either the Mohr-Coulomb criterion or the unified tensile fracture criterion. The compressive plasticity of the composites is always higher than the tensile plasticity, leading to a significant inconsistency. The enhanced plasticity of BMG composites containing ductile dendrites compared to monolithic glasses strongly depends on the details of the microstructure of the composites. A deformation and damage mechanism of pseudo-plasticity, related to local cracking, is proposed to explain the inconsistency of plastic deformation under tension and compression. Besides, significant melting on the shear fracture surfaces was observed. It is suggested that melting is a common phenomenon in these materials with high strength and high elastic energy, as it is typical for BMGs and their composites failing under shear fracture. The melting mechanism can be explained by a combined effect of a significant temperature rise in the shear bands and the instantaneous release of the large amount of elastic energy stored in the material.

Stability of the formation interface under the impact of hydraulic fracture propagation in the vicinity of the formation interface

Unconventional hydrocarbon reservoirs in layered formations,such as tight sandstones and shales,are continually being developed.Hydraulic fracturing is a critical technology for the high-efficiency development of hydrocarbon reservoirs.Understanding the stress field and stability of the formation interface is vital to understanding stress propagation,preferably before the growing hydraulic fracture contacts the formation interface.In this study,models are developed for computing the stress field of hydraulic fracture propagation near the formation interface,and the stress fields within and at the two sides of the formation interface are analyzed.Four failure modes of the interface under the impact of hydraulic fracture propagation in its vicinity are identified,and the corresponding failure criteria are proposed.By simulating the magnitude and direction of peak stress at different parameters,the failure mode and stability of the formation interface are analyzed.Results reveal that when the interface strength is weak,the formation interface fails before the growing hydraulic fracture contacts it,and its stability is significantly related to a variety of factors,including the type of formation interface,rock mechanical properties,far-field stress,structural parameters,distance between the hydraulic fracture and formation interface,and fracturing execution parameters.

Theoretical and experimental study of 3-D initial fracture and its significance to faulting

The experimental results of 3-D fracture under compression are introduced in brief and the theory of stress criterion of 3-D fracture is studied. Methods to imitate initial fractures are developed. It is pointed that there are important defects in the extreme value （EV） method ever proposed by Palaniswamy and Knauss. The major defect lies in that only two Euler angles （2EA） are considered, but another one is neglected. If the variation of all the three Euler angles （3EA） are considered, one can get better result which is consistent with the observation of faulting that extends on curved surfaces but not on planes. The method of evaluating maximal normal stress direction vector （NSDV） is proposed and further proved to be equivalent to the 3EA method. It is proved that the NSDV method can be further optimized to the method of composition of the first principal differential plane （CFPDP）. The results from CFPDP method can fit the curved surfaces of initial growth observed in the experiments of 3-D fracture. The CFPDP method can also be used to interpret the 3-D fractures of the slipping section between the asperities in the buried fault plane that is modeled as ellipse crack. The results of 3-D fracture can be applied to interpreting the related problems of faulting including the mechanism of a lot of shatter rocks with different dimensions, the cause of earthquakes occurred at the edge of plate under low shear stress, and the mechanism of anisotropy caused by the extensive dilatancy anisotropy （EDA） cracks.

Extending application of asymmetric semi-circular bend specimen to investigate mixed mode Ⅰ/Ⅱ fracture behavior of granite

The asymmetric semi-circular bend(ASCB)specimen has been proposed to investigate the cracking behavior in different geo and construction materials and attracted the attention of researchers due to its advantages.However,there are few studies on the fracture toughness determination of rock materials.In this work,a series of fracture tests were performed with the ASCB specimens made of granite.The onset of fracture,crack initiation angle and crack propagating trajectory was analyzed in detail combined with several mixed mode fracture criteria.The influence of the crack length on the mode Ⅰ/Ⅱ fracture toughness was studied.A comparison between the fracture toughness ratios predicted by varying criteria and experimental results was conducted.The relationship between experimentally determined crack initiation angles and curves of the generalized maximum tangential stress(GMTS)criterion was obtained.The fracture process of the specimen was recorded with the high-speed camera.The shortcomings of the ASCB specimens for the fracture toughness determination of rock materials were discussed.The results may provide a reference for analysis of mixed mode I and II fracture behavior of brittle materials.

Study of Debond Fracture Toughness of Sandwich Composites with Metal Foam Core

Two types of experiments were designed and performed to evaluate the adhesive bond in metal foam composite sandwich structures. The tensile bond strength of face/core was determined through the flatwise tensile test （FWT）. The test results show that the interfacial peel strength is lower than the interlaminar peel strength in FWT test. The mode I interracial fracture toughness （GIC） of sandwich structures containing a pre-crack on the upper face/core interface is determined by modified cracked sandwich beam （MCSB） experiment. It is found that the crack propagates unsynchronously on the two side of the specimen and the propagation of interfacial debonding always stays on the face/core interface during the MCSB tests. In order to simulate the failure of metal foam composite sandwich structures, a computational model based on the Tsai-Hill failure criterion and cohesive zone model is used. By comparing with experiment results, it can be concluded that the computational model can validly simulate the interracial failure of metal foam composite sandwich structures with reasonable accuracy.