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.

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 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.

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.

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.

A DUCTILE FRACTURE CRITERION BASED ON THREEDIMENSIONAL VOID MODEL

从一个显微镜的观点导出的一个破裂标准被建议并且证明了在单轴的紧张的分析有效。在一方面，预言可锻的破裂的一个方法用一个三维的空模型和速度断绝的假设被建议。在到骨折的空体积部分和批评种类之间的关系，在新模型，的帮助下计算象那的一样的趋势从修改 Thomason 获得了的表演当模特儿。在另一方面，机械并且单轴的紧张实验的 metallographic 分析用四种碳钢被执行。在到骨折的空体积部分和批评种类之间的关系，从新模型计算，与结果更好同意从实验获得了，而非那由修改 Thomason 模型计算了，它基于三维的空模型证实可锻的破裂标准的有效性。

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 investi-gated. 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, preva-lent crack length and orientation, etc.).

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.

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.

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.

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.

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 steel 0Cr18Ni9 (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.

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.

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

The deformation,damage,fracture,plasticity and melting phenomenon induced by shear fracture were investi- gated 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 plas- ticity 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.

ON PROBLEMS OF FRACTURE OF MATERIALS IN COMPRESSION ALONG TWO INTERNAL PARALLEL CRACKS

The frqcture of materials under the action of compressive forces, directed along cracks which are parallel in plere cannot be described within the framework of the linear fracture mechanics. The criteria of fracture of the Griffith-Irvin or COC type,used in classical linear fracture mechanics, are not applicable in this problem, since these forces have no influence on stress intensity coefficients and on values of cracks opening[1,2]. The problems of such a class may be described only by using new approaches.One of possible approaches is presented by the first author, which involves using linearized relations, derived from exact non-linear equations of deformable solid body mechanics[3, 4, 5]. It should be remarked here that this approach has been widely used inproblems of deformable bodies stability. As a criterion of the initiation of fracture the criterion of local instability near defects of the crack type is used. In these cases the process of loss of stability initiates the fracture process.

Anisotropy of strength and deformability of fractured rocks

Anisotropy of the strength and deformation behaviors of fractured rock masses is a crucial issue for design and stability assessments of rock engineering structures,due mainly to the non-uniform and nonregular geometries of the fracture systems.However,no adequate efforts have been made to study this issue due to the current practical impossibility of laboratory tests with samples of large volumes containing many fractures,and the difficulty for controlling reliable initial and boundary conditions for large-scale in situ tests.Therefore,a reliable numerical predicting approach for evaluating anisotropy of fractured rock masses is needed.The objective of this study is to systematically investigate anisotropy of strength and deformability of fractured rocks,which has not been conducted in the past,using a numerical modeling method.A series of realistic two-dimensional(2D) discrete fracture network(DFN)models were established based on site investigation data,which were then loaded in different directions,using the code UDEC of discrete element method(DEM),with changing confining pressures.Numerical results show that strength envelopes and elastic deformability parameters of tested numerical models are significantly anisotropic and vary with changing axial loading and confining pressures.The results indicate that for design and safety assessments of rock engineering projects,the directional variations of strength and deformability of the fractured rock mass concerned must be treated properly with respect to the directions of in situ stresses.Traditional practice for simply positioning axial orientation of tunnels in association with principal stress directions only may not be adequate for safety requirements.Outstanding issues of the present study and suggestions for future study are also presented.

A NONLOCAL THEORY FOR BRITTLE FRACTURE

In this paper,a nonlocal theory of fracture for brittle materials has been systematically devel-oped,which is composed of the nonlocal elastic stress fields of Griffith cracks of mode-Ⅰ,Ⅱ and Ⅲ,theasymptotic forms of the stress fields at the neighborhood of the crack tips,and the maximum tensile stresscriterion for brittle fracture.As an application of the theory,the fracture criteria of cracks of mode-Ⅰ,Ⅱ,Ⅲ and mixed mode Ⅰ-Ⅱ,Ⅰ-Ⅲ are given in detail and compared with some experimental data and thetheoretical results of minimum strain energy density factor.

DYNAMIC MIXED MODE FRACTURE INITIATION IN ROCK^+

In this paper, a distortion dynamic strain energy density factor criterion for dynamic mixed-mode fracture initiation in rock is suggested.The results of the investigation on 14 three-point bending (TPB) and four-point bending(FPB) rock specimens tested u

Effect of Fracture Criteria on Taylor Impact Fracture

Taylor impact test on aluminum alloy 7A04-T6 presented in a previous study has been numerically evaluated using the finite element code ABAQUS/Explicit in this paper. The influence of fracture criterion in numerical simulations of the deformation and fracture behavior of Taylor rod has been studied. The following fracture criterions, included a modified version of Johnson-Cook, the Cockcroft-Latham(C-L), the constant fracture strain, the maximum shear stress and the maximum principle stress fracture models, have been used in this paper. Model constants for each criterion are calibrated from material tests. The modified version of Johnson-Cook fracture criterion with the stress triaxiality cut-off idea used can give good prediction to the Taylor impact fracture behavior. However, the C-L fracture criterion with only a constant required for calibrating by a simple test is found to give reasonable predictions. Unfortunately, the other three criteria are not able to repeat the experimentally obtained fracture behavior. The result indicates that the stress triaxiality cut-off idea is necessary to predict the Taylor impact fracture.