Crack veolcity and acceleration effects on dynamic stress intensity factor in polymers

Dynamic crack propagations in PMMA and epoxy specimens were studied using the method of caustics in combination with a Cranz-Schardin type high-speed camera. Single-edge-cracked tensile specimens were fractured under pin-loading conditions so that cracks could experience acceleration, deceleration and re-acceleration stages in one fracture process. The dynamic stress intensity factor K _ID, crack velocity a and acceleration a were evaluated in the course of crack propagation to examine the effects of a and a on K _ID. Results showed that a and a were important factors in changing the values of K _ID, and for constant a the decelerating crack had a larger value of K _ID than the accelerating or re-accelerating crack. Also, it was found that K _ID could be expressed as two parametric functions of and a for PMMA and epoxy specimens. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dynamic crack propagation and arrest in orthotropic DCB fiber composite specimens

An orthotropic double cantilever beam (DCB) model is used to study dynamic crack propagation and arrest in 90° unidirectional Hercules AS/3501-6 graphite fiber epoxy composites. The dynamic fracture toughness of the composite is determined from tests performed on the long-strip specimen and DCB crack arrest experiments are conducted. By using the dynamic fracture toughness in a finite-difference solution of the DCB governing partial differential equations, a numerical solution of the crack propagation and arrest events is computed. Excellent agreement between the experimental and numerical crack arrest results are obtained.     

Analytical modelling of dynamic fracture and crack arrest in DCB specimens under fixed displacement conditions

An analytical solution via the beam theory considering shear deformation effects is developed to solve the static and dynamic fracture problem in a bounded double cantilever beam (DCB) specimen. Fixed displacement condition is prescribed at the pin location under which crack arrest occurs. In the static case, at first, the compliance function of a DCB specimen is obtained and shows good agreement with the experimental results cited in the literature. Afterward, the stress intensity factor is determined at the crack tip via the energy release rate formula. In the dynamic case, the obtained governing equations for the model are solved supposing quasi‐static treatment for unstable crack propagation. Finally, a closed form expression for the crack propagation velocity versus beam parameters and crack growth resistance of the material is found. It is shown that the reacceleration of crack growth appears as the crack tip approaches the finite boundary. Also, the predicted maximum crack propagation velocity is significantly lower than that obtained via the Euler–Bernoulli theory found in the literature.     

An experimental cum numerical technique to determine dynamic interlaminar fracture toughness

A method combining experimental and finite element analysis is developed to determine interlaminar dynamic fracture toughness. An interlaminar crack is propagated at very high speed in a double cantilever beam (DCB) specimen made of two steel strips which are bonded together by epoxy with a precrack of about 40 mm length. The face of the front cantilever is bonded to a large solid block and a special fixture is designed to apply impact load to the rear cantilever through a load bar. In the load bar, a compressive square shaped elastic stress pulse is generated by impacting it with a striker bar which is accelerated in an air gun. The rear cantilever is screwed to the load bar; when the incident compressive pulse reaches the specimen, a part of the energy is reflected into the load bar and the rest of it passes to the specimen. By monitoring the incident and the reflected pulses in the load bar through strain gauges, deflection of cantilever-end is determined. The crack velocity is determined by three strain gauges of 0.2 mm gauge length bonded to the side face of the rear cantilever. Further, the first strain gauge, bonded very close to the tip of the precrack, and the crack velocity determine the initiation time of crack propagation.

The experimental results are used as input data in a finite element (FE) code to calculate J-integral by the gradual release of nodal forces to model the propagation of the interlaminar crack. The initiation fracture toughness and propagation fracture toughness are evaluated for an interlaminar crack propagating with a velocity in the range of 850 to 1785 m/s. The initiation toughness and propagation toughness were found to vary between 90–200 J/m² and 2–13 J/m², respectively.     

A phenomenological analysis of Mode I fracture of adhesively-bonded pultruded GFRP joints

The fracture behavior of adhesively-bonded pultruded joints was experimentally investigated under Mode I loading using double cantilever beam specimens. The pultruded adherends comprised two mat layers on each side with a roving layer in the middle. An epoxy adhesive was used to form the double cantilever beam specimen. The pre-crack was introduced in three different depths in the adherend in order to induce crack initiation and propagation between different layers and thus investigate the effect of these different crack paths on the strain energy release rate. Short-fiber and roving bridging increased the fracture resistance during crack propagation. Specific levels of critical strain energy release rates could be attributed to each of the crack paths, with their levels depending on the amount of short-fiber bridging and the presence of a roving bridge. The different levels of critical strain energy release rate could be correlated to the morphology of the fracture surface and the strain energy release rate can thus be determined visually without any measurement.     

Energy absorption mechanisms during dynamic fracturing of fibre-reinforced composites

Dynamic photoelastic experiments were conducted to study crack propagation in fibrereinforced materials and, in particular, to determine the energy losses occurring during the crack growth and arrest process. This study utilized modified compact tension specimens which were fabricated from polyester matrix and different reinforcing fibres. The effect of the fibre-matrix interface on energy absorbed was also studied. The energy absorbed was partitioned into two parts: that absorbed in the fracture process zone associated with the crack tip, and the energy lost outside this zone. Results show that fibre reinforcement reduces the energy absorbed in the fracture process zone by about 10% for well-bonded and 15% for partly debonded fibres. For the same initial strain energy, this reduction in fracture energy manifests itself in reduced K _ID and lower crack-jump distance as compared to monolithic specimens. Reinforced specimens are found to retain a higher strain energy after crack arrest. The energy absorbed outside the fracture process zone for monolithic and well-bonded fibres is about 45% of the initial strain energy, while for partly debonded fibres it is about 55%.     

Arrest and propagation of a brittle crack in structural steels. Report 2

The authors describe a laboratory method of determining the fracture toughness of structural steel in the crack propagation stage K_ID. The K_ID — a dependences were obtained for three structural ferritic-pearlitic and bainitic steels at different temperatures. The K_ID — a dependences are analyzed from the viewpoint of microstructural features of failure of these materials.     

Some considerations of asymmetric cracking in an applied-moment double cantilever beam

In situ observations of crack propagation in applied-moment double cantilever beam specimens have been used to obtain the R-curve behaviour of Si₃N₄/50% BN–50% Al₂O₃ laminated composites, in which the BN–Al₂O₃ layers function as weak interphases. The crack plane and the crack direction were, respectively, normal and parallel to the plane of the laminated layers. During crack propagation, both delamination and crack deviation from the centreline of the specimen occurred. A deviated crack resulted in an uneven moment of inertia in the two beams of the specimen. For a non-laminated material, a deviated crack would become unstable, such that the crack would propagate towards the beam with the smaller moment of inertia. It was found in the present study that delamination in a laminated composite can stabilize the propagation of a deviated crack. The stabilization of a deviated crack with delamination was due to a decrease in the inequality in the moment of inertia of the two beams compared to that without delamination.     

双悬臂梁试件裂纹动态扩展的准静态数值分析

本文采用双悬臂梁（DCB）试件研究了复合材料层合板层间插入韧性胶膜（Interleaf）层的Ⅰ型断裂行为。试验结果表明,含和不含Interleaf层试件分别呈现脆性非稳态和脆性稳态分层扩展特性。针对非稳定裂纹扩展问题,依据动态断裂力学中应变能释放率与动能变化率的关系,提出了以断裂韧性值G_IC变化来抵消动能变化对裂纹扩展过程影响的准静态分析方法,根据试验中裂纹扩展的韧性变化,推导出适用于准静态裂纹扩展模拟的等效韧性G_IC*,利用ABAQUS平台和虚裂纹闭合技术（VCCT）建立了三维有限元计算模型;实现了从起裂到止裂的整个裂纹动态扩展过程的数值模拟,揭示了非稳定裂纹扩展过程中一些复杂的力学现象。      

A local modulus analysis of rapid crack propagation in polymers

This work is concerned with the analysis of rapid crack propagation (RCP) in Polymethylmethacrylate (PMMA), Polycarbonate (PC) and two-layer PMMA/PC systems. Remarkably constant crack speeds were observed, and higher crack speeds corresponded to the higher preloads. Uniform fracture surfaces were associated with these constant speed RCPs. An indirect method was used to characterise dynamic fracture properties of the materials. The method relies on the recorded crack length histories and boundary conditions which are incorporated in a dynamic Finite Element (FE) code to generate the crack resistance (G _ID). The numerical simulation of the constant speed RCPs generated highly scattered G _ID data. Very large variations of the computed G _ID with the crack length did not correspond to fracture surface appearances. Geometry dependent and multivalued crack resistance results with respect to the crack speed cast doubt on the uniqueness of G _ID. In this work, attempts were made to overcome these difficulties by exploring the concept that the anomalies arise from large local strains around the rapidly moving crack tip, resulting in the crack seeing a low local modulus. It is demonstrated that the critical source of error on the analysis of RCP, is the improper linear elastic representation of the material behaviour around the propagating crack tip. Since the parameters describing the behaviour of the materials near the propagating crack tip were unknown, local non-linear effects were approximated by a local low modulus strip along the prospective crack path. The choice of the local modulus was justified by measurements of the strain histories along the crack path during RCP. The local strip low modulus model generated a larger amount of the kinetic energy in the sample and the crack resistance was reduced compared to results from the single constant modulus approach. Most importantly, G _ID data were nearly independent of the crack length, crack speed and the specimen size. This local modulus concept was also successfully applied to the analysis of RCP in the duplex specimen configuration.     

Thickness dependence of Gc for shear lip propagation from a single crack propagation specimen: aluminium 6061-T6 alloy,cold-rolled copper and BPA polycarbonate

Values ofG _c for ductile crack propagation in a series of double cantilever beam specimens, each with a single side groove of constant depth, increase linearly with net section thickness. If a single side groove with linearly varying depth is cut in a double cantilever beam specimen, the tapered net section thickness results in a plastic zone, the crosssection area of which increases linearly with crack length. The attendantG _c increases in proportion to the plastic zone size in such a specimen. A single properly designed tapered section specimen appears to be capable of providing estimates of (a) the dependence of shear lipG _c on shear lip width, (b) the natural shear lip width and shape, and (c) the shear lip plastic strain. G _c and plastic zone data from specimens of both kinds are reported for aluminium 6061-T6 alloy, cold-rolled copper and BPA polycarbonate. Results of uniaxial tensile tests and of centre-notch tensile tests are also reported for comparison purposes.G _cs, plastic zone sizes and plastic zone strains vary from material to material and appear to reflect in part the drawing and necking characteristics seen in uniaxial tensile tests.     

Study of mode I interlaminar fracture in CFRP laminates by moiré interferometry

Moiré interferometry was utilized to study mode I interlaminar fracture in double cantilever beam specimens of unidirectional carbon fiber/epoxy composites. The crack opening displacement was experimentally determined in the vicinity of the crack tip to evaluate the distortion at the beam root of the specimen. The beam root distortion was found to make an important contribution to increasing the value of crack opening displacement. The effect of the beam root distortion on the evaluation of fracture toughness value was also examined.     

Study of mode I crack dynamic propagation behaviour and rock dynamic fracture toughness by using SCT specimens

To study crack dynamic propagation behaviour and rock dynamic fracture toughness, a single cleavage triangle (SCT) specimen was proposed in this paper. By using these specimens and a drop‐weight test system, impact experiments were conducted, and the crack propagation velocity and the fracture time were measured by using crack propagation gauges. To examine the effectiveness of the SCT specimen and to predict the test results, finite difference numerical models were established by using AUTODYN code, and the simulation results showed that the crack propagation path agrees with the test results, and crack arrest phenomena could happen. Meanwhile, by using these numerical models, the crack dynamic propagation mechanism was investigated. Finite element code ABAQUS was applied in the calculation of crack dynamic stress intensity factors (SIFs) based on specimen dimension and the loading curves measured, and the curves of crack dynamic SIFs versus time were obtained. The fracture toughness (including initiation toughness and propagation toughness) was determined according to the fracture time and crack speeds measured by crack propagation gauges. The results show that the SCT specimen is applicable to the study of crack dynamic propagation behaviour and fracture toughness, and in the process of crack propagation, the propagation toughness decreases with crack propagation velocity, and the crack arrest phenomena could happen. The critical SIF of an arrest crack (or arrest toughness) was higher than the crack propagation toughness but was lower than the initiation toughness.     

Influence of intralaminar cracking on the apparent interlaminar mode I fracture toughness of cross‐ply laminates

One of the major difficulties in interlaminar fracture tests of multidirectional laminates is the high tendency for intralaminar cracking and the resulting wavy crack propagation. Experimental work showed that this occurred in double cantilever beam (DCB) tests of cross‐ply laminates having a starter crack on a 0°/90° interface. Moreover, under steady‐state propagation conditions, the apparent values of the critical strain energy release rate G_Ic were two times higher than those of 0°/0° specimens. In this paper, a finite‐element‐based progressive damage model was used to simulate crack propagation in cross‐ply specimens. The results showed that transverse cracking alone cannot be responsible for the above difference of G_Ic values. Therefore, the higher propagation G_Ic values for cross‐plies must be attributed to the more extensive fibre bridging observed and to plastic deformations of the 90° interfacial ply.     

Crack path selection in adhesively bonded joints: the roles of external loads and speciment geometry

This paper investigates the roles of external loads and specimen geometry on crack path selection in adhesively bonded joints. First, the effect of mixed mode fracture on crack path selection is studied. Using epoxy as an adhesive and aluminum as the adherends, double cantilever beam (DCB) specimens with various T-stress levels are prepared and tested under mixed mode fracture loading. Post-failure analyses on the failure surfaces using X-ray photoelectron spectroscopy (XPS) suggest that the failure tends to be more interfacial as the mode II fracture component in the loading increases. This fracture mode dependence of the locus of failure demonstrates that the locus of failure is closely related to the direction of crack propagation in adhesive bonds. Through analyzing the crack trajectories in failed specimens, the effect of mixed mode fracture on the directional stability of cracks is also investigated. The results indicate that the direction of the crack propagation is mostly stabilized when more than 3% of mode II fracture component is present at the crack tip regardless of the T-stress levels in the specimens for the material system studied. Second, using a high-speed camera to monitor the fracture sequence in both quasi-static and low-speed impact tests, the effect of debond rate on the locus of failure and directional stability of cracks is investigated. Post-failure analyses including XPS, Auger electron spectroscopic depth profile, and scanning electron microscopy indicate that as the crack propagation rate increases, the failure tends to be more cohesive and the cracks tend to be directionally unstable. Last, as indicated by the finite element analyses results, the T-stresses, and therefore the directional stability of cracks in adhesive bonds, are closely related to the thickness of the adhesive layer and also the thickness of adherend. This specimen geometry dependence of crack path selection is studied analytically and is verified experimentally.     

A criterion of crack propagation in timber

For reasons of likeness with specimens used for the drafting of standards in France, a DCB (Double cantilever beam) specimen has been studied in order to determine its possibilities to estimate the toughness of wood. Firstly comparison of critical loads of natural cracks and of narrow slits is made. Secondly, the Rice integral has been evaluated at crack initiation in TL (tangential longitudinal) and RL (radial longitudinal) modes of fracture. The methods of fitting the energy curves have been compared. Thirdly, the critical stress intensity factor K_IC has also been obtained in these two directions of loading.     

Mode I and mode II initiation fracture toughness and resistance curve of medium density fiberboard measured by double cantilever beam and three-point bend end-notched flexure tests

Using specimens of medium density fiberboard, double cantilever beam and three-point bend end-notched flexure tests were conducted to obtain the mode I and mode II initiation fracture toughness and resistance curve for in-plane and through-the-thickness systems. The mode I initiation fracture toughness was smaller than that of mode II for the in-plane crack systems, but this tendency was inverse for the through-the-thickness systems. The fracture toughness increased during the crack propagation because of the significant fiber bridgings induced between the crack surfaces, but the increase of the mode I propagation fracture toughness was moderated after the crack reached a certain length. In contrast, the mode II propagation fracture toughness continuously increased during the crack propagation.     

A new data reduction scheme for mode I wood fracture characterization using the double cantilever beam test

This paper describes experimental and numerical studies on double cantilever beam test applied to fracture characterization of wood in mode I. A new data reduction scheme based on the beam theory and specimen compliance is proposed in order to overcome the difficulties inherent to crack monitoring during propagation. A cohesive damage model adapted to wood is used to simulate the test. The cohesive properties are evaluated using an inverse method based on a developed Genetic Algorithm through an optimisation strategy. The results demonstrate the effectiveness of the proposed methodology as a suitable data reduction scheme for the double cantilever beam test.     

Tapered beam on elastic foundation model for compliance rate change of TDCB specimen

A modified beam theory is developed to predict compliance rate change of tapered double cantilever beam (TDCB) specimens for mode-I fracture of hybrid interface bonds, such as polymer composites bonded to wood. The analytical model treats the uncracked region of the specimen as a tapered beam on generalized elastic foundation (TBEF), and the effect of crack tip deformation is incorporated in the formulation. A closed-form solution is obtained to compute the compliance and compliance vs. crack length rate change. The present TBEF model is verified with finite element analyses and experimental calibration data of compliance for wood-wood and wood-composite bonded interfaces. The compliance rate change can be used with experimental critical fracture loads to determine the respective critical strain energy release rates or fracture toughness of interface bonds. The present analytical model, which accounts for the crack tip deformation, can be efficiently and accurately used for compliance and compliance rate-change predictions of TDCB specimens and reduce the experimental calibration effort that is often necessary in fracture studies. Moreover, the constant compliance rate change obtained for linear-slope TDCB specimens can be applied with confidence in mode-I fracture tests of hybrid material interface bonds.