An analysis of the crack tip fields in a ductile three-point bend specimen subjected to impact loading

Analyses of an impact fracture test of a precracked, three-point beam of HY100 steel were performed to determine the dynamic fracture toughness. During impact, the crack tip opening displacement (CTOD) 100 μm behind the crack tip was measured using an optical measuring device called the interferometric strain/displacement gage. Since fracture initiates when stress wave effects dominate, a numerical simulation of the fracture event was conducted to obtain relevant near crack tip field parameters. The specimen was modeled by a plane stress finite element simulation using a rate sensitive elastoplastic material law. Since the simulated CTOD was to be compared with the measured CTOD in a region of residual strains due to crack closure, this effect was included in the model. The simulation produces a CTOD versus time response within 10% of the observed response, indicating that the other field quantities (such as the J-integral) should also be reliable. The loading rate /.K₁ was approximately 8 × 10⁶MPa√m/sec. If the fracture initiation time is assumed to coincide with the time at which the simulated and observed CTOD curves diverge, then the impact fracture toughness is 56% higher than the static fracture toughness.     

Analysis of the dynamic responses for a pre-cracked three-point bend specimen

In this paper, shear deformation and rotary inertia was introduced into the calculation of the dynamic stress intensity factor by means of solving the stiffness of a pre-cracked three-point bend specimen. A simple formula of dynamic stress intensity factor for a pre-cracked three-point bend specimen is derived using the vibration analysis method. Dynamic three-point bending tests were performed on a uniquely modified Hopkinson pressure bar, allowing the dynamic responses of the pre-cracked specimen, such as: the natural frequency, the period of apparent specimen oscillations, the dynamic loads, and the dynamic stress intensity factor to be analyzed experimentally and theoretically.     

The effect of an elliptical inclusion on a crack

The interaction between an elliptical inclusion and a crack is analyzed by body force method. The investigated stress field is simulated by superposing the fundamental solutions for a point force applied at a point in an infinite plate containing an elliptical inclusion. Based on numerical results, effects of the inclusion shape on the crack tip stress intensity factor are discussed. It is found that for small cracks emanating from a stress-higher point on the inclusion interface the stress intensity factors are mainly determined by the stresses, occurring at the crack starting point before the crack initiation, and the inclusion root radius, besides the crack length. However, for the cracks occurring in a stress-lower region around the inclusion, it is difficult to characterize the effect of the inclusion geometry on the stress intensity factors of small cracks by the inclusion root radius alone. This revised version was published online in July 2006 with corrections to the Cover Date.     

A three-dimensional finite element analysis of the three-point bend specimen

A finite element analysis of an elastic three-dimensional specimen similar to the three-point bend specimen used in fracture testing has been performed. Special crack front elements which contain the proper square root singularity are used in the analysis. Stress intensity factors have been calculated for many values of the crack size and show considerable dependence on the thickness. The effects of Poisson's ratio and the free surface which are usually neglected in the two-dimensional analysis are also discussed.     

The effect of crack front curvature and side-grooving on three point bend specimen fracture toughness measurements

Finite element simulations of the three point bend fracture toughness specimen have been performed to investigate the effect of crack front curvature and side-grooving. Even modest crack front curvature moves the position of maximum energy release rate from the center towards the free surfaces of the specimen. A 30 percent difference between the maximum and minimum crack length can double the maximum energy release rate compared to that calculated for a straight crack of the same average length. A correction curve has been derived from which the curved crack energy release rate can be obtained using two dimensional solutions. Deep side-grooving substantially increases the energy release rate at the root of the groove, but for groove depths no more than 30 percent of the section, an energy release rate can be estimated from the two dimensional ungrooved solution scaled by the ratio of ungrooved to grooved thicknesses.     

Compliance crack length relations for the four-point bend specimen

Compliance crack length relations for the four-point bend specimen geometry have not been reported in the literature in spite of this geometry being one of the popularly used specimens for fatigue crack growth studies. An effort has been made in the present work to fill this gap. Accordingly, the finite element technique was employed to simulate loading and calculate displacements at various locations in a four-point bend specimen. The load-displacement data thus obtained were processed to yield compliance crack length relations. These relations were employed to calculate the crack length during fatigue testing of four-point bend specimens in which the crack length was also measured by optical means. A good correlation was observed between the predicted crack length and that measured optically.     

Numerical evaluation of stress intensity factor and J integral in three-point bend specimen

The present paper attempts to evaluate the fracture mechanics parameters, the stress intensity factor (K) and Rice's energy integral (J) in plane strain conditions for three-point bend specimens. Both the parameters have been evaluated by the FEM using higher order isoparametric elements (i.e. quadratic elements). The crack tip elastic singularity (1/√r) has been taken into account by the use of the special crack tip elements of degenerate triangular element type as well as the fine eight-noded isoparametric plane elements. The stress distribution has been compared with the Westergaard solution in the vicinity of the crack. The K and J values have also been-compared with the theoretical results.     

Higher order terms of the crack tip asymptotic field for a notched three-point bend beam

The coefficients of the first five terms of the crack tip asymptotic field of three-point bend single edge notched beams (TPBs) with span to depth ratios widely used in testing are computed using a hybrid crack element (HCE), which has the potential to directly calculate not only the stress intensity factor (SIF) but also the coefficients of the higher order terms of the crack tip asymptotic field. The general approximate closed-form expression for SIF proposed by Guinea et al. (1998) and the available numerical results for the second T-term are calibrated by the results of the HCE. Approximate analytical expressions for the second, third, fourth and fifth terms for a TPB with a span to depth ratio of 4 and for a single edge notched beam subjected to pure bending are obtained by fitting the computed data. These approximations are then used to predict the general expressions for coefficients of the higher order terms of a TPB with arbitrary span to depth ratio . The accuracy of these general expressions is studied for TPBs with =6, 8 and 12.     

The effect of a rigid elliptical inclusion on a straight crack

The general problem of a straight crack near a rigid elliptical inclusion is solved. Complex potentials presented in a previous paper (Santare and Keer [6]) for the interaction of an edge dislocation with rigid ellipse are used to formulate the Green's function for this problem. The solution is written as a set of singular integral equations for crack opening displacement which are solved numerically. Stress intensity factors are presented for a variety of crack/inclusion geometries.     

三点弯曲试验弯剪耦合效应分析及测试结果修正方法

三点弯曲试验中存在着弯剪耦合效应,通过引入弯剪耦合系数,利用Tsai-Hill强度准则建立弯剪耦合方程,定量分析了弯剪耦合作用,提出了复合材料三点弯曲试验结果修正方法。研究表明：弯剪耦合效应会对复合材料三点弯曲试验结果产生比较大的影响。在弯剪耦合效应作用下,弯曲强度测试误差随弯剪强度比的增大而增大,剪切强度的测试误差随弯剪强度比的增大而减小。当弯剪耦合系数一定时,由耦合引起的测试误差的大小取决于梁的跨高比与材料的弯剪强度比的比值。对试验结果修正后,增加了不同跨高比下的三点弯曲试验结果的可比性,反映了材料的固有属性。     

A 3-D finite element analysis of a chevron-notched,three-point bend fracture specimen for ceramic materials

A 3-D finite element analysis of a chevron-notched, three-point bend specimen was used to determine the load point displacement (LPD) and the crack mouth opening displacement (CMOD) for four initial crack-depth-to-width ratios of the chevron notch. Relations between the LPD and CMOD specimen compliances, as functions of crack length, were developed and the LPD compliance versus crack length relations were compared with previous analyses. In addition, the LPD compliance versus crack length relations are used to modify previously developed geometry correction factors for the stress intensity factor.The LPD/CMOD relations are then applied to calculate the LPD from the CMOD measured during the fracture testing of silicon nitride and silicon carbide chevron-notched, three-point bend specimens. The work-of-fracture values for the two ceramic materials are compared using the calculated and the measured LPD. The fracture toughness values are compared as calculated from the modified and the unmodified geometry correction factors for the stress intensity factor. Finally, the crack growth resistance curves are determined from the fracture test data.

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Résumé Sur une éprouvette de flexion sur trois points entaillée en chevron, on a fait usage de l'analyse par éléments finis à trois dimensions pour déterminer le déplacement au point d'application de la charge (LPD) et le déplacement d'ouverture des bords de la fissure (CMOD) correspondant à quatre rapports de profondeur sur largeur de fissure pour l'entaille en chevron. On a établi les relations de compliance entre le LPD et le CMOD en fonction de la longueur de fissure et on a comparé les relations de compliance entre le LPD et la longueur de fissuration avec celles résultant d'analyses antérieures. En outre, ces dernières relations ont été utilisées en vue de modifier les coefficients de correction géométrique précédemment établis pour le facteur d'intensité de contrainte.On applique ensuite les relations LPD/CMOD au cacul du LPD à partir du CMOD mesuré au cours d'essais de rupture en flexion sur trois points d'éprouvettes en nitrure de silicium et en carbure de silicium entaillées en chevron. On compare les valeurs du travail de rupture des deux matériaux céramiques en utilisant les valeurs de LPD calculées et mesurées. On compare les valeurs de la ténacité à la rupture obtenues par le calcul à partir des coefficients de correction de la géométrie modifiés ou non modifiés. Enfin, on détermine les courbes de résistance à la croissance des fissures à partir des données de rupture.

     

The interaction between a crack and an inclusion

A numerical method described recently[1] is used here to obtain the stress intensity factor for a crack near an inclusion. Results for the variation of the stress intensity factor with the distance of the crack tip from the inclusion, are shown graphically.     

The effect of filler loading and process route on the three-point bend performance of waste based composites

The three-point bend behaviour of polyester resin composites loaded with high volume fractions of recycled waste materials has been investigated to determine the effect of composition and processing route on performance.

Flyash powder and quarry waste were chosen as candidate fillers. Fillers were added either separately or combined. Three-point bend specimens were manufactured by conventional gravity mould casting, by degassing prior to casting or by vibration moulding. The addition of filler to the resin matrix resulted in a steady reduction in ultimate flexural strength from approximately 85 MPa for the pure resin to approximately 40 MPa for 50% filled material. As filler levels were increased above this level, the strength rapidly decreased. A corresponding increase in flexural stiffness with increasing filler amount was also evident.

For a given amount of filler, flexural strength decreased with increasing particulate filler size. The flexural modulus appeared to be unaffected.

The effect of matrix reinforcement on the performance of heavily filled (>75% by volume) polyester resin is also presented. Matrix reinforcement resulted in the production of high strength/high modulus materials with filler contents up to 75% and it is envisaged that these filler ratios can by further increased without a loss of flexural strength.     

316L三点弯曲试样动静态断裂韧性对比实验研究

为研究316L型不锈钢的动静态断裂韧性,该文使用Instron-4505万能材料试验机对含有预制裂纹的316L型不锈钢试样进行准静态三点弯曲实验,测得其准静态断裂韧性应力强度因子K_I=53.34 MPam,同时基于霍普金森压杆(SHPB)技术对该材料三点弯曲试样进行动态断裂韧性的实验研究,测得其在3种不同加载率下的动态断裂韧性应力强度因子。结果表明:316L型不锈钢是率敏感材料,随着加载率的增加,该材料的动态断裂韧性呈下降趋势,且其断裂力学性能优良,可在工程实际中广泛应用。