Failure analysis of quasi-isotropic CFRP laminates under high strain rate compression loading

Dynamic compressive strength of quasi-isotropic fiber composite is investigated experimentally and also numerically simulated. In-plane compression tests at strain rates around 400/s quasi-isotropic laminates were performed using the Split Hopkinson Pressure Bar (SHPB). The material system used was Texipreg^® HS160 REM, comprising high strength unidirectional carbon fiber and epoxy resin. The dynamic strength of quasi-isotropic laminates exhibits a considerable increase when compared to the static values. The finite-element model used ABAQUS™ three-dimensional solid elements C3D8I with 8 nodes and user-defined interface finite elements with 8 nodes [Gonçalves JPM, de Moura MFSF, de Castro PMST, Marques AT. Interface element including point-to-surface constraints for three-dimensional problems with damage propagation. Eng Comp: Int J Comput Aided Eng Software 2000;17(1):28–47; de Moura MFSF, Pereira AB, de Morais AB. Influence of intralaminar cracking on the apparent interlaminar mode I fracture toughness of cross-ply laminates. Fatigue Fract Eng Mater Struct 2004;27(9):759–66.]. These interface elements which connect the three-dimensional solid elements modeling the composite layers, include a cohesive damage model allowing the simulation of delamination initiation and propagation. Hence the present model assumes that the phenomenon of failure under these conditions is mainly dictated by interface delamination. This is supported by experimental tests which showed that all quasi-isotropic laminates split into several almost intact sublaminates. The model compares very well with experimental results, confirming the formulated hypothesis that the internal layer damage does not markedly contribute to the quasi-isotropic laminate failure.     

Failure mode transition in ceramics under dynamic multiaxial compression

An experimental technique based on the Kolsky pressure bar has been developed to investigate the behavior of ceramics under dynamic multiaxial compression. Experimental results for aluminum nitride (AlN), together with data available in the literature, indicate that a Mohr-Coulomb criterion and the Johnson–Holmquist model fit the experimental data for failure in a brittle manner, whereas the ceramic material exhibited pressure insensitive plastic flow at high pressures. A failure surface is constructed which represents the material failure behavior, including brittle failure, brittle/ductile transition and plastic flow, under various pressures. The effect of various material properties on the failure behavior was investigated. The Poisson's ratio is found to be a measure of brittleness for ceramic materials with low spall strength under shock wave loading conditions. Lower value of Poisson's ratio indicates that the material will fail in a brittle manner through axial splitting even under uniaxial strain loading; whereas materials with higher Poisson's ratio may be expected to deform plastically beyond the Hugoniot Elastic Limit (HEL). The applicability of the proposed failure surface to a range of ceramics is explored and the limitations of the model are outlined. This revised version was published online in July 2006 with corrections to the Cover Date.     

Energy absorption capability of carbon nanotubes dispersed in resins under compressive high strain rate loading

The focus of the present study is on energy absorption capability (E_A) of carbon nanotubes (CNTs) dispersed in thermoset epoxy resin under compressive high strain rate loading. Toward this objective, high strain rate compressive behavior of multi-walled carbon nanotube (MWCNT) dispersed epoxy is investigated using a split Hopkinson pressure bar. The amount of MWCNT dispersion is varied up to 3% by weight. Calculation methodology for the evaluation of E_A of individual CNTs and CNTs dispersed in resins/composites is presented. Quantitative data on E_A of individual CNTs and CNTs dispersed in resins under quasi-static and high strain rate loading is given.     

Failure initiation at a blunt V-notch tip under mixed mode loading

A criterion to predict crack onset at a sharp V-notch tip in homogeneous brittle materials under a mixed-mode loading was presented and validated by experimental observations in a previous paper by the authors. This criterion slightly underestimates the experimental loads causing failure which is attributed to a small notch tip radius that blunts the sharp corner. This discrepancy is rigorously analyzed mathematically in this paper by means of matched asymptotics involving 2 small parameters: a micro-crack increment length and the notch tip radius. A correction is brought to the initial prediction and a better agreement is obtained with experiments on PMMA notched specimens.     

Measurement and prediction of compressive properties of polymers at high strain rate loading

Strain-rate effect is widely recognized as a crucial factor that influences the mechanical properties of material. Despite the acknowledge importance, the understanding of how such factor interact with the sensitivity of the polymers in terms of mechanical properties is still less reported. In this study, an experimental technique, based on the compression split Hopkinson pressure bar, was introduced to perform high strain rate testing, whereas, a conventional universal testing machine was used to perform static compression testing, to experimentally investigate the independent and interactive effects of strain rates towards mechanical properties of various polymers. Based on the experimental results, we parameterized two equation models, which were used to predict the yield behavior of tested polymer samplings. The experimental results indicate that, the yield stress, compression modulus, compressive strength, strain rate sensitivity and strain energy increased significantly with increasing strain rates for all tested polymers. Meanwhile, the yield strain and the thermal activation volume exhibit contrary trend to the increasing strain rates. Interestingly, the proposed constitutive models were almost agreed well with experimental results over a wide range of strain rate investigated. Of the three polymers, polypropylene shows the highest strain rate sensitivity at static and quasi-static region. On the other hand, at dynamic region, polycarbonate shows the highest strain rate sensitivity than that of polypropylene and polyethylene. Overall, both experimental and numerical models proved that the mechanical properties of polymer show significant sensitivity and dependency towards applied strain rates up to certain extent.     

The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading

The purpose of this paper is to revisit the maximum tensile stress (MTS) criterion to predict brittle fracture for mixed mode conditions. Earlier experimental results for brittle fracture of polymethylmethacrylate (PMMA) using angled cracked plates are also re-examined. The role of the T -stress in brittle fracture for linear elastic materials is emphasized. The generalized MTS criterion is described in terms of mode I and II stress intensity factors, K _I and K _II and the T- stress (the stress parallel to the crack), and a fracture process zone, r _c . The generalized MTS criterion is then compared with the earlier experimental results for PMMA subjected to mixed mode conditions. It is shown that brittle fracture can be controlled by a combination of singular stresses (characterized by K ) or non-singular stress ( T -stress). The T -stress is also shown to have an influence on brittle fracture when the singular stress field is a result of mode II loading.     

Experimental fracture investigation of CNT/epoxy nanocomposite under mixed mode II/III loading conditions

For the first time, the brittle fracture of epoxy‐based nanocomposite reinforced with MWCNTs (multi‐walled carbon nanotubes) and subjected to mixed mode II/III loading conditions is investigated. This experimental investigation is carried out using a newly developed test configuration. Araldite LY 5052 epoxy, which is a resin frequently used in aerospace industry, is utilized to fabricate pure epoxy and nanocomposite test specimens with two different MWCNTs contents of 0.1 and 0.5 wt%. The obtained experimental results reveal that adding MWCNTs to epoxy resin up to 0.5 wt% improves the fracture toughness under pure mode II and pure mode III loading with an increasing trend. This is while the improvement under mixed mode II/III loading is reduced by adding nanotubes more than 0.1 wt%. To justify the variations of fracture toughness in terms of nanoparticles content, SEM (scanning electron microscopy) photographs of the fracture surfaces of the specimens in the vicinity of the initial crack front are prepared. Additional fracture mechanisms caused by adding carbon nanotubes are discussed in detail based on the provided SEM images.     

中应变率加载下云杉各向异性力学行为研究

采用高速加载INSTRON设备对云杉开展10⁰ s^-1~10² s^-1中应变率压缩实验,研究了材料沿顺纹、横纹径向、弦向、以及径(弦)切面内与顺纹呈15°、30°、45°、60°和75°夹角方向的力学性能。实验表明随着加载方向由顺纹向横纹径(弦)向变化,材料屈服强度逐渐减小,应力-应变曲线塑性流动段由\     

Dynamic expansion modeling of a thick-walled cylinder under internal high strain rate loading

This article presents analysis of the dynamic behavior of a thick-walled cylinder under the assumption of nonlinear strain rate hardening behavior under high strain rate loading before any fracture on the surface. The theoretical model applies both to direct and indirect use of dynamic strength of material and instant boundary conditions to establish a differential equation for radial expansion velocity. Further, detailed discussion will be given with emphasis on the main aspects of the cylinder behavior, i.e., radial displacement, internal pressure, strain rate, flow stress, radial and tangential stress, and the influence of the different material rate sensitive exponent.     

Impact behavior and constitutive model of nanocrystalline Ni under high strain rate loading

To investigate mechanical properties and deformation mechanisms of nanocrystalline materials under high strain rate, dynamic impact tests for nanocrystalline Ni bulk prepared by high-energy ball milling combined with compaction and hot-pressure sintering were carried out under different high strain rates on Split Hopkinson bar. Compared with the testing results under quasi-static strain rate, the nanocrystalline Ni has higher strength under high strain rate. Meanwhile, the impact stress–strain curves exhibit rate-dependence strength and light strain hardening behavior. Subsequently, a mechanism of dislocation gliding in combination of grain boundary sliding was discussed and a constitutive model was built under high strain rate loading based on the mechanism. The predictions of the constitutive model under high strain rates show good agreements with the experimental data. Finally, the properties of the nanocrystalline Ni were discussed in detail.     

高应变率加载下玻璃板碎片尺寸的理论模型

基于材料损伤理论和损伤断裂机理,分析了普通平板玻璃在高应变率下的损伤破碎规律。根据玻璃碎片破坏损伤应变能和断裂表面能之间的平衡关系,推导了不同应变率下预测玻璃碎片大小的计算公式。该模型能够直接、定量地给出玻璃板中由于裂缝间的贯通形成的平均碎片大小,同时能够求出玻璃碎片的数量。对于该模型,讨论了玻璃板尺寸及临界应变等因素对玻璃碎片大小的影响。     

A new fixture for fracture tests under mixed mode I/II/III loading

In this paper, a new loading device for general mixed mode I/II/III fracture tests is designed and recommended. Finite element analyses are conducted on the proposed apparatus to evaluate the fracture parameters of the tested samples under various mixed mode loading conditions. The numerical results revealed that the designed loading fixture can generate wide varieties of mode mixities from pure tensile mode to pure in‐plane and out‐of‐plane shear modes. The accuracy of the proposed fixture is evaluated by conducting a wide range of fracture tests on compact tension shear (CTS) specimens made of polymethyl methacrylate (PMMA). The experimental results are then compared with the theoretical predictions obtained by the Richard criterion. A good consistency is observed between the experimental results and theoretical predictions.     

Fracture behaviour of plain and fiber-reinforced concrete with different water content under mixed mode loading

In the present paper, plain concrete and fiber-reinforced concrete are considered from the point of view of the mechanical characteristics, with particular emphasis on the fracture resistance, for different values of the water/cement ratio and different amount and type (metallic or polymeric) of reinforcing fibers. The main mechanical characteristics (such as compressive strength and tensile strength) of the examined materials have experimentally been determined, and several pre-cracked specimens have been tested under three-point bending up to the final failure in order to study the fracture behaviour by also evaluating the fracture energy. Furthermore, the crack paths for static tests under displacement control have been obtained, and the load–displacement deflection curves have been determined for different crack configurations. Assuming the fracture surface characterised by a fractal dimension, some quantitative evaluations of the fracture energy are carried out. Then, the fracture behaviour and the post-peak behaviour of plain and fiber-reinforced specimens are discussed, and the effects of reinforcing fibers are quantified. Some conclusions are finally drawn.     

Modeling of dynamic expansion of thick‐walled cylinder under high strain rate loading with strain rate sensitivity analysis

This paper presents an analysis of the dynamic behavior of thick‐walled cylinder using Levy‐Mises flow rule in the assumption of a non‐linear strain rate hardening behavior under high strain rate loading. The theoretical model to be developed in this work applies indirect use of dynamic strength of material characterized by a non‐linear relation and instant boundary condition based on Jones‐Wilkins‐Lee equation of state to establish differential equation for radial expansion velocity. Detailed discussion will be given with emphasis on the main aspects of the cylinder behaviour, i.e. radial displacement, internal pressure, strain rate, flow stress, radial and tangential stress and the influence of different material rate sensitive exponent. Results show a good agreement with the analytical solutions proposed here.     

On the failure of cracks under mixed-mode loads

Fracture of plates containing a crack under mixed-mode, I and II, loading conditions is investigated. Fracture mechanisms are first examined from fracture surface morphology to correlate with the macroscopic fracture behavior. Two distinct features are observed and they are typical of shear and tensile types of failure. From this correlation, a fracture criterion based on the competition of the attainment of a tensile fracturing stress σ_{_C} and a shear fracturing stress τ_{_C} at a fixed distance around the crack tip is proposed. Material ductility is incorporated using τ_{_C}/σ_{_C} determined from classical material failure theories. The type of fracture is predicted by comparing τ_{_max}/σ_{_max} at r=r_{_C} for a given mixed mode loading to the material ductility_{τ_C/σ_C} , i.e. τ_{_max}/σ_{_max})<(τ_{_C} /σ_{_C}) for tensile type of fracture and (τ_{_max}/σ_{_max}) r (τ_{_C}/ σ_{_C}) for shear type of fracture. It is found that, for typical engineering structural metals with certain ductility, (1) crack propagation initiates according to the maximum hoop stress criterion when the the mode mixity is near mode I and according to the maximum shear stress criterion when the mode mixity is near mode II, and (2) the transition of the failure from tensile to shear type can be predicted by the proposed criterion. For brittle materials the maximum hoop (opening) stress always reaches the tensile fracturing stress before the maximum shear stress reaches the shear fracturing stress of the material at a crack tip. Therefore, specimens made of brittle materials tend to fail under the maximum hoop stress criterion, as demonstrated by Erdogan and Sih (1963) and others. This revised version was published online in August 2006 with corrections to the Cover Date.     

Computational comparisons of homogeneous and statistical descriptions of AerMet100 steel subjected to high strain rate loading

In order to simulate the effect of material microstructure a statistically compensated Johnson-Cook (JC) fracture model has been implemented into the Eulerian shock physics code, CTH. This model uses a Weibull function to produce a distribution of initial failure strains within the JC fracture model. A parametric analysis where the Weibull modulus was systematically varied was conducted on two sets of experimental fragmentation data. The first experiment consisted of an explosively loaded cylinder of AerMet100. The second was an expanding tube experiment which used a plastic cylinder to load the AerMet100 and provided a problem at a lower strain rate. In both sets of experiments, the fragments were soft captured for later examination. While CTH does not explicitly track fragments, a post processor written at the Naval Surface Warfare Center Dahlgren Division was used to calculate the mass of each of the fragments in the expanding debris cloud. The results were analyzed and compared back to baseline homogeneous calculations. The use of a statistically compensated JC fracture model substantially improved the fragment mass distribution for the explosively loaded cylinder. However, the lower strain rate expanding tube showed only minimal improvement. A probable reason for this limitation and future analysis are discussed.     

Two parameter approach for elastic-plastic fracture of short cracked specimens under mixed mode loading

For mode-I loading, in order to describe the near-tip stress field in a specimen under large scaled yielding, two parameter approaches such as J-T, J-Q and J-A₂ theories have been developed and proved well for their validity and limit. In this work elastic-plastic finite element analysis were performed to investigate the effects of mode mixity and T-stress upon near-tip stress distribution for a small-scale-yield model with the modified boundary layer and CTS (Compact Tension-Shear) configuration under large-scale-yield state. As the results, some peculiar characteristics were found as follows; As the mode mixity increases, normal stresses _rr and near the crack tip in the small-scale-yield model get significantly affected by the positive T-stress as well as the negative T-stress, while the shear stress _r is little affected by T-stress. Also, the near-tip stress distribution of short cracked CTS specimens under the large-scale-yield state agree fairly well with that of the small-scale-yield model with an appropriate positive T-stress. The two parameters approach with J-integral and T-stress seems to be a good tool for describing the near-tip stress field under a mixed mode loading and large-scale-yield state.     

Quasi-static and high strain rate response of aluminum matrix syntactic foams under compression

Aluminum alloy matrix syntactic foams were produced by inert gas pressure infiltration. Four different alloys and ceramic hollow spheres were applied as matrix and filler material, respectively. The effects of the chemical composition of the matrix and the different heat-treatments are reported at different strain-rates and in compressive loadings. The higher strain rates were performed in a Split-Hopkinson pressure bar system. The results show that, the characteristic properties of the materials strongly depends on the chemical composition of the matrix and its heat-treatment condition. The compressive strength of the investigated foams showed a limited sensitivity to the strain rate, its effect was more pronounced in the case of the structural stiffness and fracture strain. The failure modes of the foams have explicit differences showing barreling and shearing in the case of quasi-static and high strain rate compression respectively.     

Investigation of ductile rupture in U‐notched Al 6061‐T6 plates under mixed mode loading

The aim of the present research is to evaluate ductile failure of U‐notched components under mixed mode I/II loading conditions. For this purpose, first, several rectangular plates made of the aluminium alloy Al 6061‐T6 and weakened by central bean‐shaped slit with two U‐shaped ends are tested under mixed mode I/II loading conditions, and the load‐carrying capacity of the specimens are experimentally measured. Then, using the equivalent material concept, Al 6061‐T6, which is a highly ductile material, is equated with a virtual brittle material, and the load‐carrying capacity of the same U‐notched specimens virtually made of the equivalent material is theoretically predicted by using two well‐known stress‐based brittle fracture criteria. Finally, the theoretical failure loads of the virtual specimens are compared with the experimental ones of the real Al 6061‐T6 specimens. It is revealed that the experimental results could very well be predicted by means of both brittle fracture criteria without conducting time‐consuming elastic–plastic analyses.     

Ductile fracture mechanism of low-temperature In-48Sn alloy joint under high strain rate loading

The failure behaviors of In-48Sn solder ball joints under various strain rate loadings were investigated with both experimental and finite element modeling study. The bonding force of In-48Sn solder on an Ni plated Cu pad increased with increasing shear speed, mainly due to the high strain-rate sensitivity of the solder alloy. In contrast to the cases of Sn-based Pb-free solder joints, the transition of the fracture mode from a ductile mode to a brittle mode was not observed in this solder joint system due to the soft nature of the In-48Sn alloy. This result is discussed in terms of the relationship between the strain-rate of the solder alloy, the work-hardening effect and the resulting stress concentration at the interfacial regions.