预制裂纹角度对橡胶拉伸断裂影响的有限元分析

初始裂纹的形态影响着裂纹尖端的应力场和扩展方向,进而决定着橡胶材料的使用寿命。目前人们关于预制裂纹试样拉伸断裂的研究主要集中在直裂纹,很少涉及预制裂纹角度的改变对橡胶拉伸断裂的影响。文中应用ANSYS有限元分析软件计算拉伸状态下含不同裂纹角度橡胶试样裂纹尖端的等效应力值和撕裂能的大小,判断裂纹是否扩展及扩展方向,并对橡胶试样进行拉伸验证试验测试。结果表明,在拉伸断裂过程中,裂纹尖端的应力值和撕裂能随着初始预制裂纹角度的增大而增大,裂纹尖端形状均由初始的尖点变成圆弧状;含不同裂纹角度橡胶试样的拉伸断裂形貌与裂纹预测扩展方向基本一致,验证了有限元分析的正确性。     

Orientation and loading condition dependence of fracture toughness in cortical bone

The fracture toughness at crack initiation were determined for bovine cortical bone under tension (mode I), shear (mode II), and tear (mode III). A total of 140 compact tension specimens, compact shear specimens and triple pantleg (TP) specimens were used to measure fracture toughness under tension, shear, and tear, respectively. Multiple-sample compliance method was utilized to measure the critical strain energy release rate (G_c) at the a/W=0.55 (crack length, a, to specimen width, W, ratio). The critical stress intensity factor (K_c) was also calculates from the critical loading (P_c) of the specimens at the a/W=0.55. The effect of the anisotropy of bone on its resistance to crack initiation under shear and tear loading was investigated as well. Fracture toughness of bone with precrack orientations parallel (designed as longitudinal fracture) and vertical (designed as transverse fracture) to the longitudinal axis of bone were compared. In longitudinal fracture, the critical strain energy release rate (G_c) of cortical bone under tension, shear, and tear was 644±102, 2430±836, and 1723±486 N/m, respectively. In transverse fracture, the critical strain energy release rate (G_c) of cortical bone under tension, shear, and tear was 1374±183, 4710±1284, and 4016±948 N/m, respectively. An unpaired t-test analysis demonstrated that the crack initiation fracture toughness of bone under shear and tear loading were significantly greater than that under tensile loading in both longitudinal and transverse fracture (P<0.0001 for all). Our results also suggest that cortical bone has been “designed” to prevent crack initiation in transverse fracture under tension, shear, and tear.     

Failure assessment of notched polycrystalline graphite under tensile-shear loading

The fracture load and the fracture initiation angle were experimentally measured for a V-notched specimen made of polycrystalline graphite under combined tensile-shear loading. The experimental results were obtained for several specimens with different notch angles and various notch tip radii. The experimental observations showed that for a constant notch tip radius, the fracture load in pure tensile loading conditions decreases as the notch angle increases. Moreover, for a constant notch angle, as the notch tip radius increases the fracture load in graphite specimens enhances in the entire domain between pure tensile and pure shear loading conditions. A recently developed failure criterion was then used to estimate the experimental values of the notch fracture resistance and the fracture initiation angle for the tested graphite specimens. The experimental results could be estimated very well by using the results of the proposed criterion.     

Experimental studies on mixed‐mode dynamic fracture behaviour of aluminium alloy plates with narrow U‐notch

Mixed‐mode dynamic fracture behaviour of cast aluminium alloy ZL205A thin plates with narrow U‐notch was studied by split Hopkinson tensile bar apparatus. Specimens with different loading angles were designed to realize different fracture modes. The same loading condition was maintained during the tests. Recovery specimens show that crack propagates along the notch direction. Force–elongation relations show that with the loading angle increasing, the fracture force increases while the final elongation decreases. Deformation and fracture process was observed by a high‐speed camera. Displacement distribution around the crack was calculated through digital image correlation technique. Based on the photos and displacement results, initiation time of the crack was derived. Besides, two stress components (normal stress and shear stress) applied on the fracture surface were investigated. Results show that crack initiation stresses at different loading angles satisfy the ellipse equation. Pure mode I and II fracture stresses are 425.3 and 236.7 MPa, respectively. Furthermore, specific fracture energy of different specimens was calculated. The energy data vary with loading angle and located on an approximate upward parabolic curve. From the curve, the minimum specific fracture energy of the thin plate specimen is 42.0 kJ/m² under loading angle of 76.3°.     

Experimentelle und numerische Ermittlung dynamischer Risswiderstandskurven im Kerbschlagbiegeversuch

Experimental and numerical determination of crack resistance curves in the notched‐bar impact test The assessment of the reliability of components requires the knowledge of crack resistance curves, which are often not available due to lack of specimen material. More likely is the availability of typical material parameters such as the yield strength, tensile strength, uniform elongation, elongation at rupture as well as upper shelf impact energy and the lateral elongation of notched‐bar impact test specimens. The material model of Gurson describes ductile crack growth due to the nucleation, growth and coalescence of voids in the material. Although dependent on the material and temperature, the material parameters of the Gurson model are independent of the specimen geometry and rate of loading. This latter fact allows one to use the values of these parameters determined on statically‐loaded fracture mechanics specimens to model specimens with other geometries and subjected to different loading conditions, in particular to model impact loaded Charpy‐V specimens. A method is proposed to construct crack resistance curves based on available data of tension tests and on quasi‐static yield curves. Dynamic yield curves are determined using proven procedures as based on the analysis of the dislocation activation energy. The ductile damage parameters are then obtained via simulation of tests on notched tensile specimens and notched‐bar impact tests as well as the fitting to the upper shelf impact energy. In this way, the ductile damage parameters are determined, which in turn enable the determination of the required J‐resistance curves via simulation of ductile crack growth in fracture mechanics specimens. Thus, the application of the classical J‐integral concept gets possible. Furthermore, the independence of the identified material parameters from the geometry of the specimen then allows the use of the Gurson model to analyse the safety of structural components with cracks directly.     

Determination of the fracture energy of a composite by the method of digital speckle correlation

We have developed a computational-and-experimental procedure for evaluating the fracture energy of composite materials, which lies in the determination of surface displacements in a neighborhood of the tip of a stress concentrator under static tension by the method of digital speckle correlation. Using the known displacement distribution, we calculate strains in the prefracture zone as well as the opening and shear of crack lips for given loading force and measuring base. The static tensile stress-strain diagram, together with the established specimen strain, enables us to find stresses in the prefracture zone. Using these data, we find the fracture energy of the composite. We also present some results of investigations for a three-layer composite material based on an epoxy-phenol plastic reinforced chaotically with disperse particles.     

Fracture analysis of dissimilar Al‐Al friction stir welded joints under tensile/shear loading

In this research, fracture of dissimilar friction stir welded (FSWed) joint made of Al 7075‐T6 and Al 6061‐T6 aluminum alloys is investigated in the cracked semi‐circular bend (CSCB) specimen under mixed mode I/II loading. Due to the elastic‐plastic behavior of the welded material and the existence of significant plastic deformations around the crack tip at the propagation instance, fracture prediction of the FSWed specimens needs some failure criteria in the context of the elastic‐plastic fracture mechanics which are very complicated and time‐consuming. For this purpose, the Equivalent Material Concept (EMC) is used herein by which the tensile behavior of the welded material is equated with that of a virtual brittle material. By combining EMC with the 2 brittle fracture criteria, namely the maximum tangential stress (MTS) and mean stress (MS) criteria, the load‐carrying capacity (LCC) of the FSWed CSCB specimens is predicted. Comparison of the experimental results and theoretical predictions from the 2 criteria showed that both criteria could accurately predict the LCC of the cracked specimens. Moreover, as the contribution of mode II loading increases, the size of the plastic region around the crack tip at failure increases, leading to increasing the LCC.     

Dynamic fracture of a beam or plate under tensile loading

The dynamic fracture response of a long beam of brittle elastic material under tensile loading is studied. If the magnitude of the applied loading is increased to a critical value, a crack is assumed to propagate across the beam cross section. In a parallel analysis to [t] the crack length and applied loading at the fracture face are determined as functions of time measured from fracture initiation. The results of the analysis are shown in graphs of crack length, crack tip speed and fracturing section tensile loading vs time. As found in [1], the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then decelerates rapidly in the final stage of the process. Finally, by appropriate change of the elastic modulus, the results may be applied to plane strain fracture of a plate under pure tensile loading.     

Evaluation of dynamic fracture toughness parameters of locomotive axle steel by instrumented Charpy impact test

The analysis of the energy of fracture of specimens from steel OSL, which is widely used for the manufacture of railway axles under shock loading, is performed. The nature and quantitative parameters of the typical stages of the processes of plastic and brittle fracture, depending on the test temperature and stiffness of the stress state at the tip of the crack‐like defect, are established. It is shown that impact loading at 20 °C leads to the formation of the local zone of plasticity and ductile–brittle fracture of the material. An increased stiffness of the stress state at the tip of the defect at ?40 °C causes brittle fracture. An approach is developed, which is based on using the size of shear lips as a quantitative parameter of fracture under normal and low temperatures, similar in its physical essence to deformation approaches of nonlinear fracture mechanics. Based on this approach and the quantitative analysis of specimen fracture zones, the physical and mechanical scheme of specimen fracture is proposed in the presence of localized plasticity and in its absence near the tip of the concentrator.     

Fracture initiation at a crack or notch in a viscoplastic material under high rate loading

The two-dimensional problem of an edge crack in a half space or plate is considered. The body is loaded by a suddenly applied, spatially uniform normal velocity imposed on the plane boundary of the body on one side of the edge crack. Otherwise, the boundary of the body, including the crack faces, is traction free. Both cases of an initially sharp crack tip and a narrow notch with small but nonzero notch root radius are considered. The material is modeled as elastic viscoplastic, including strain hardening, rate sensitivity and thermal softening. The applied loading produces predominantly mode II loading in the crack tip region. Under these conditions it is possible to nucleate an adiabatic shear band at the crack tip as a precursor to a mode II fracture. On the other hand, because of the rate sensitivity of the material and the high rate of loading, it may be possible under certain conditions to generate tensile stresses in the crack tip region sufficiently large to nucleate brittle tensile fracture. The problem is solved numerically by means of the finite element method in order to investigate the competition between these two possible fracture initiation mechanisms. The magnitude of the impact velocity imposed on the edge of the plate and the notch tip acuity have an effect on processes near the crack tip. For given material, the inception of crack growth is determined by the competition between a stress-based brittle fracture condition, associated with rate sensitivity and strain hardening, and a strain based criterion, associated with high strain rate and thermal softening.     

Strain rate dependence of HPFRCC cylinders in monotonic tension

High-Performance Fiber-Reinforced Cementitious Composite (HPFRCC) materials exhibit strain hardening in uniaxial, monotonic tension accompanied by multiple cracking. The durability of HPFRCC materials under repeated loading makes them potentially suitable for seismic design applications. In this paper, the strain rate dependence of tensile properties of two HPFRCC materials in cylindrical specimens is reported from a larger study on strain rate effects in tension, compression and cyclic tension–compression loading. The cylindrical specimens were loaded in monotonic tension at strain rates ranging from quasi-static to 0.2 s⁻¹. To evaluate the impact of specimen geometry on tensile response, coupon specimens loaded in monotonic tension under a quasi-static strain rate were compared to corresponding cylindrical specimens made from the same batch of material. Tensile strength and ductility of the HPFRCC materials were significantly reduced with increasing strain rate. Multiple cracking, strain hardening, strain capacity, and the shape of the stress–strain response were found to be dependent on specimen geometry. SEM images taken of the fracture plane of several specimens indicated that pullout and fracture of the fibers occurred for both HPFRCC materials studied here.     

Dynamic crack propagation in large steel specimens

Dynamic fracture experiments on crack initiation and crack growth in single edge bend specimens are performed. The impact velocity is in the range of 14 to 50 m/s and the specimen size is 320×75 mm with a thickness varying from 18 to 40 mm. The experiments are recorded by high speed photography.Two different steel qualities are investigated and their constitutive characterisation are obtained from uni-axial tension tests and shear tests with strain rates in the range 10⁻⁴ to 10³ s⁻¹ and tension tests at temperatures between −196 and 600°C.One of the materials exhibits a transition from a ductile dimple fracture to a brittle cleavage fracture as the loading velocity increases and as the specimen thickness increases. Scanning electron microscope fractographs show that the density of plastic bridges within cleavage ligaments decreases with increasing impact velocity and with increasing specimen thickness. It is also noted that the local crack propagation direction deflects from the global one in cleavage fracture areas with a high density of plastic bridges.The other material fails in a ductile mode in all the investigated cases.     

Effect of shear and rotary inertia on dynamic fracture of a beam or plate in tensile loading

The dynamic fracture response of a long beam of brittle material subjected to tensile loading is studied. If the magnitude of the applied tensile loading is increased to a critical value, a crack will propagate from one of the longitudinal surfaces of the beam. As an extension of previous work, the effect of shear and of rotary inertia on the tensile loading and the induced bending moment at the fracturing section is included in the analysis. Thus an improved formulation is presented by means of which the crack length, crack tip velocity, bending moment and axial force at the fracture section are determined as functions of time after crack initiation. It is found that the rotary effect diminishes the bending moment effect and retards total fracture time whereas the shear has an opposite effect. Thus by combining the two effects (to simulate to first order the Timoshenko beam) overall fracture is retarded. The results also apply for plane strain fracture of a plate in tensile loading provided the value of the elastic modulus is appropriately modified.     

Characterization of High‐Strain Rate Mechanical Behavior of AZ31 Magnesium Alloy Using 3D Digital Image Correlation

Characterization of the material mechanical behavior at sub‐Hopkinson regime (0.1 to 1 000 s^?1) is very challenging due to instrumentation limitations and the complexity of data analysis involved in dynamic loading. In this study, AZ31 magnesium alloy sheet specimens are tested using a custom designed servo‐hydraulic machine in tension at nominal strain rates up to 1 000 s^?1. In order to resolve strain measurement artifacts, the specimen displacement is measured using 3D Digital Image correlation instead from actuator motion. The total strain is measured up to ≈ 30%, which is far beyond the measurable range of electric resistance strain gages. Stresses are calculated based on the elastic strains in the tab of a standard dog‐bone shaped specimen. Using this technique, the stresses measured for strain rates of 100 s^?1 and lower show little or no noise comparing to load cell signals. When the strain rates are higher than 250 s^?1, the noises and oscillations in the stress measurements are significantly decreased from ≈ 250 to 50 MPa. Overall, it is found that there are no significant differences in the elongation, although the material exhibits slight work hardening when the strain rate is increased from 1 to 100 s^?1.     

Effect of bending moment on the dynamic fracture of a beam or plate under tensile loading

The dynamic fracture response of a long beam of brittle elastic material under tensile loading is studied. If the magnitude of the applied loading is increased to a critical value, a crack is assumed to propagate across the beam cross section. As an extension of previous work, an induced bending moment generated during fracture is incorporated into the analysis and this improved formulation is presented. The crack length, crack tip speed, axial force and bending moment on the fracturing section are determined as functions of time after crack initiation. It is found that the bending moment has a significant effect on the fracture process in that it tends to retard fracture and causes a drastic change in the slope of the loading curve for large crack depths. Finally, by appropriate change of the elastic modulus, the results may be applied to plane strain fracture of a plate in pure tensile loading.     

Fracture studies on polypropylene

Measurements of fracture surface energy have been made on polypropylene in the undrawn state and at different states of orientation over the temperature range ?60 to 60° C. Tear tests were employed and it was found that the fracture surface energy of unoriented material was of the order of 10⁴ to 10⁵ J m^?2. As orientation (represented by birefringence) increased, the fracture surface energy decreased by a factor of approximately 100 at room temperature but this factor was found to decrease with decreasing temperature. For all degrees of orientation, the fracture surface energy increased with increasing temperature in the range ?60 to 60°C, Scanning electron microscope studies showed a direct relation between the crack tip diameter and the fracture surface energy of unoriented specimens. From comparable studies on the tearing of rubber, Thomas has interpreted such a relationship as implying that the high values of fracture surface energy arise from the energy required to deform the material in the crack tip up to the breaking point. On this basis the reduction in fracture surface energy with increase in orientation may be regarded as being due to the associated diminution of the crack tip diameter. This interpretation is substantiated by direct measurements of crack tip diameter for specimens of intermediate and high orientation. Further microscopic studies of fracture surfaces indicate three modes of fracture which have been correlated with the appearance of the crack tip and tend to occur in certain ranges of birefringence.     

Debonding and crack kinking in foam core sandwich beams—I. Analysis of fracture specimens

Sandwich beam specimens, recently developed for the study of facing/core debond fracture, were analyzed using the finite element method. Peel fracture was approached using a modified double cantilever beam (DCB) sandwich specimen with a precrack between the facing and core, while shear fracture employed a modification of the ASTM block shear test to include a facing/core precrack. Complex and conventional stress intensity factors were calculated for bimaterial cracks located between facing and bondlayer and bondlayer and core over a large range of core moduli. Overall, much larger stress intensity factors were observed for an interfacial crack between the facing and bondlayer than for a crack between the bondlayer and core for both types of specimens. Crack kinking analysis of the DCB specimen revealed that the debond tends to remain interfacial for stiff core materials, but may deflect into the core for compliant core materials. In shear loading of a debonded sandwich beam it was demonstrated that crack kinking is possible for any core material.     

Fracture toughness measurement of thin-film silicon

The fracture toughness of single‐crystal silicon thin films oriented to (100) and (110) was investigated by tensile testing under both 〈100〉 and 〈110〉 loading conditions. The specimen was fabricated from a p‐type Czochralski (CZ)‐grown wafer and passed through a thermal process during the fabrication of the test device. The measured fracture toughness is dependent on the loading direction in the tensile test and independent of the specimen surface orientation. The test results were 1.94 MPa√m in the 〈100〉 direction and 1.17 MPa√m in the 〈110〉. In these tests, no longitudinal size effect on the fracture stress or fracture toughness was observed. The SEM photographs obtained from the fracture specimens after the tensile test show that the crack initiated from the notch tip and propagated straight in the across‐the‐width direction on the (110) or (111) cleavage plane.     

Subcritical crack propagation under cyclic stress impulse

An equipment has been designed to observe subcritical crack propagation under cyclic impulse (impact) loads. The equipment design uses the concept of stress wave propagation in bars. A four point bend notched specimen is struck by an incident bar with a known stress wave. The test specimens were machined from PMMA sheet (Lucite^®). The crack, initiated from the notch, was detected by a step wise increase of a graphitic grid imprinted on one side of the specimen. The data was analyzed using fracture mechanics theory and compared with that of conventional fatigue.Although the applied strain rate was quite high (1s^–1), stable crack propagation was significant. It appears that the elastic energy stored in the specimen within the duration of each impulse is dissipated in craze formation at the tip of the advancing crack. Furthermore, the magnitude of stable crack propagation was larger under impulse loading than under sinusoidal fatigue. On the other hand, cracks were slower under impulse loading. Fractographic evidence attributes these phenomena to the nature of craze growth under each loading condition.