Penetration and failure of lead and borosilicate glass against rod impact

This paper presents the experimental design and results for gold rod impact on DEDF (5.19 g/cm³) and Borofloat (2.2 g/cm³) glass by visualizing simultaneously failure propagation in the glass with a high-speed camera and rod penetration with flash radiography. At a given impact velocity, the velocity of the failure front is significantly higher during early penetration than during steady-state penetration of the rod. For equal pressures but different stress states, the failure front velocities determined from Taylor tests or planar-impact tests are greater than those observed during steady-state rod penetration. The ratio of average failure front velocity to rod penetration velocity decreases with increasing impact velocity (v_p) in the range of v_p=0.4–2.8 km/s. As a consequence, the distance between the rod tip and the failure front is reduced with increasing _vp$v_{\mathrm{p}}$. The Tate term R_T increases with impact velocity.     

Failure and penetration response of borosilicate glass during short-rod impact

A series of reverse ballistic experiments reveal further properties of the failure front (FF) associated with the penetration of borosilicate glass by a gold rod. Importantly, the FF ceases to propagate a short time after the rod is fully eroded. The rods, 1 mm in diameter, were short (5–11 mm). The glass targets were 20-mm diameter cylinders, 60-mm or 100-mm long. Impact velocities varied between 1 and 2 km/s. The impact and penetration process was observed with five flash X-rays and a 16-frame high-speed optical camera. A FF propagates from the impact region. The velocity of FF propagation is an increasing function of the impact velocity. The termination of the FF can reasonably be predicted in most cases with a simple model that assumes a rarefaction wave, originating at the time of complete rod erosion, propagates from the bottom of the penetration channel to the FF at a speed equal to the bulk wave speed of undamaged glass.     

Characterization of heterogeneous materials under shear loading at finite strain

This article presents a homogenization procedure to predict the effective shear response of heterogeneous materials at large deformation. Assuming local periodicity, heterogeneous microstructure is identified by a representative volume element that is subjected to an equivalent macroscopic deformation field. The energy balance and periodicity conditions are considered to relate macro and micro-stress fields. Based on the symmetrical planes of the microstructure and local periodicity, it is shown that the analysis of one-quarter of three-dimensional representative volume element is enough to evaluate the effective shear response at finite deformation. A computational method is subsequently developed to obtain the shear response of heterogeneous microstructures. The homogenization procedure is implemented to evaluate shear response of two specific heterogeneous materials, elastomeric composite and reinforced viscoelastic fluid. The performance is successfully verified by comparison of the deformation in the macroscopic level to the response of a homogenized cell.     

Failure criterion for laminated glass under impact loading and its application in finite element simulation

A failure criterion for laminated glass in case of impact is presented. The main idea of this criterion is that a critical energy threshold must be reached over a finite region before failure can occur. Afterwards crack initiation and growth is based on a local Rankine (maximum stress) criterion. The criterion was implemented in an explicit finite element solver. Different strategies for modeling laminated glass are also discussed.To calibrate the criterion and evaluate its accuracy, a wide range of experiments with plane and curved specimens of laminated glass were done. For all experiments finite element simulations were performed. The comparison between measured and simulated results shows that the criterion works very well.     

Transverse shear modulus and strength of honeycomb cores

The transverse shear mechanical behavior and failure mechanism of aluminum alloy honeycomb cores are investigated by the single block shear test in this paper. The transverse shear deformation process of honeycomb cores may be approximately categorized into four stages, namely elastic deformation, plastic deformation, fracture of cell walls and debonding of honeycomb cores/facesheets. The elastic deformation of unit cell under transverse shear displacement is also investigated by the finite element method, and the result shows that the bending deformation of the cell walls is similar to that of the cantilever beam. In order to precisely predict the equivalent transverse shear modulus and strength, not only shear deformation but also bending deformation of cell walls should be considered. Therefore, in the present paper, the equivalent transverse shear modulus and strength are predicted by application of the cantilever beam theory and thin plate shear buckling theory in conjunction with simplifying assumption as to the displacement in the cores. It is concluded that the contribution of bending deformation of cell walls to equivalent transverse shear modulus and strength is obvious with the decreasing height of cell walls.     

Modes of dynamic shear failure in solids

The technique of loading edge cracks by edge impact (LECEI) for generating high rates of crack tip shear (mode-II) loading is presented. The LECEI-technique in combination with a gas gun for accelerating the impactor is used to study the high rate shear failure behaviour of three types of materials. Epoxy resin (Araldite B) shows failure by tensile cracks up to the highest experimentally achievable loading rate; steel (high strength maraging steel X2 NiCoMo 18 9 5) shows a failure mode transition: at low rates failure occurs by tensile cracks, at higher rates, above a certain limit velocity, failure by adiabatic shear bands is observed; aluminum alloy (Al 7075) shows failure due to shear band processes in the high rate regime, but this failure mode is observed over the entire range of lower loading rates, even down to quasi-static conditions. Characteristics of the failure modes are presented. When transitions are observed in the failure process from tensile cracks to shear bands the limit velocity for failure mode transition depends on the bluntness of the starter crack the failure is initiated from: The larger the bluntness of the starter crack the higher the critical limit velocity for failure mode transition. The data indicate that adiabatic shear bands require and absorb more energy for propagation than tensile cracks. Aspects of the energy balance controlling mode-II instability processes in general are considered. Effects very different than for the mode-I instability process are observed: When failure by a tensile crack occurs under mode-II initiation conditions, a notch is formed between the initiated kinked crack and the original starter crack, and, at this notch a compressive stress concentration builds up. The energy for building up this stress concentration field is not available for propagation of the initiated kinked crack. The energy density of a mode-II crack tip stress field, however, when compared to an equivalent mode-I crack tip field, is considerably larger, and, consequently, the remaining driving energy for any mode-II initiated failure process, nevertheless, is higher than for the case of equivalent mode-I initiation conditions. Furthermore, mode-II crack tip plastic zones are considerably larger than equivalent mode-I crack tip plastic zones. Consequently, validity conditions for linear-elastic or small scale yielding failure behaviour are harder to fulfill and possibilities for the activation of nonlinear high energy ductile type failure processes are enhanced. Speculations on how these effects might favour failure by high energy processes in general and by shear bands processes in particular for conditions of high rate shear mode-II loading are presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Experimental studies on shear failure of freeze-bonds in saline ice: Part I. Set-up, failure mode and freeze-bond strength

The strength of freeze-bonds in thin saline ice has been investigated through two series (in 2008 and 2009) of experiments in the Hamburg Ship Model Basin (HSVA) as a function of the normal confinement (σ), the submersion time (Δt) and the initial ice temperature (T_i). The freeze-bonds were mostly formed in a submerged state, but some were also formed in air. The experimental set-up was improved in the 2009 experiments. In 2008 a ductile-like failure mode dominated (78%), whereas in 2009 the brittle-like dominated (93%). We suggest that this is a combined ice and test set-up effect. The 2009 experimental procedures allowed for careful sample handling giving higher strength and it was softer. Both these things should provoke a more brittle-like force-time response. The average freeze-bond strength in brittle-like samples was around 9 kPa while in ductile-like samples was around 2 kPa. The maximum freeze-bonds strength were measured for short submersion times, from 1 to 20 min, and reached a maximum value of 30 kPa.A Mohr-Coulomb like failure model was found appropriate to represent the freeze-bond shear strength as function of the normal confinement. Saline freeze-bonds in saline water had cohesion/friction angle around 4 and 1.4 kPa/25° for the brittle- and ductile-like samples respectively, which fitted well with previously published data.A bell-shape dependence for τ_c vs. Δt was found, which agreed with the predictions by Shafrova and Høyland (2007). We suggest that this is essentially a freeze-bond porosity effect and propose three phases in time with subsequent cooling, heating and equilibrium to account for this trend. Qualitative experiments showed that the submersion time and the initial ice temperature were strongly coupled.To account for the connection between contact time, block dimensions and ice properties and the freeze-bond strength, dimensionless number were used. Fourier scaling was more appropriate than Froude scaling to scale freeze-bonds.The freeze-bonding made in air developed fast (in less than 30 s) when the ice was cold and dry, but no freeze-bonding occurred for the same contact times when the ice was warm and wet.     

Modelling of damage and failure of glass/epoxy composite plates subject to impact fatigue

An investigation has been carried out to study the impact fatigue damage of glass/epoxy laminated composites. Accumulation of damage, such as matrix cracking, delamination and fibre breakage, with repeated impact of the composite material may reduce the overall stiffness. These damage modes have been combined in a very complicated way to describe damage growth and fracture. A model is proposed for characterising the damage as a function of the normalised impact number. The scalar variable D, which characterises the material damage, is written as a function of the life duration β, using a modified form of the Mankowsky empirical law [Int J Solids Struct 32(11) (1995) 1607]. The macroscopic failure mode and the internal damage in laminated specimens of glass/epoxy as a consequence of impact fatigue are analysed at different levels of incident impact energy. The impact fatigue tests have been conducted on an apparatus built in our laboratory.     

Analysis of composite skin/stiffener debounding and failure under uniaxial loading

In this paper, damage mechanisms in the composite bounded skin/stiffener constructions under monotonic tension loading are investigated. The approach uses experiments to detect the failure mechanisms, two and three-dimensional stress analysis to determine the location of first matrix cracking and computational fracture mechanics to investigate the potential for cracks and delamination growth. The laminates strength and damage mechanisms obtained from both experimental and finite elements analysis are presented for several laminates lay-up configurations. Observations on the performed experiments show matrix crack initiation and propagation in the skin and near the flange tip, causing the flange to almost fully debounded from the skin in some cases, interlaminar debounding and fiber breakage up to the failure of the components. The finite elements analysis is also show that the matrix cracks are initiated in the first skin layer for most of the cases. With increasing the applied load the matrix cracks are propagated through the thickness to reach the next layer and causes delamination between the two layers. With increasing the applied load this delamination is propagated up to the occurrence of unstable delamination growth or the first fiber breakage known as the final failure of the component. The obtained experimental failure loads are compared with those calculated by the finite elements analysis.     

Experimental and numerical study of cylindrical triaxial test on mono-sized glass beads under quasi-static loading condition

This paper aims at studying the shear behavior of homogeneous granular materials by conventional triaxial test. The work is performed both in laboratory tests and by discrete element method simulations. Conventional triaxial tests are performed on glass beads packing, while a cylindrical rigid wall boundary condition based on lame formula and a series of procedures are proposed to simulate the conventional triaxial test. The experimental results on dry and saturated glass beads samples have been studied to find out the effect of saturation condition on the shear behavior. The comparisons between experimental and numerical results show that the numerical model can reproduce deviatoric curves satisfactorily in experimental conditions as long as experimental sample remains cylindrical. It correctly describes the volumetric strains of a numerical sample up to the peak value. Additionally, a parametric study on the influence of main micromechanical parameters has been carried out, which has been compared to experimental tests with glass beads of different textures. The comparison highlights the significant effect of friction coefficients and rolling resistance coefficients on global behavior of granular materials.     

Damage mechanisms and failure modes in cross-ply laminates under monotonic tensile loading: The influence of fiber sizing

In this study, the effect of fiber-matrix interphase on the damage modes and failure mechanisms in (0, 90₃), cross-ply graphite-toughened epoxy laminates is investigated. Two material systems (designated as 810 A and 810 O) with the same fiber and same matrix, but with different fiber sizings, were used to study the effect of the interphase. The system designated as 810 A contained an unreacted Bisphenol-A (epoxy) sizing, while a thermoplastic polyvinylpyrrolidone (PVP) sizing was used in the 810 O system. Damage accumulation in the cross-ply laminates under monotonic tensile loading was monitored using edge replication, x-ray radiography, acoustic emission, optical and scanning electron microscopy. Results indicate that the fiber-matrix bond strength is lower in the 810 O system compared to the 810 A system. Transverse matrix cracking initiates at a significantly lower stress level in the 810 O laminate. The 810 O laminates also exhibit longitudinal splitting, while the stronger bonding suppress this damage mode in the 810 A laminates. Numerous local delamination occur on the 0/90 interface at the intersection of 0 and 90 degree ply cracks, in the 810 O laminates. These are absent in the 810 A laminates. The failure modes are also different in the two material systems used in this study. The 810 A laminate exhibits a brittle failure, controlled by the local stress concentration effects near broken fibers. In the 810 O laminates, the presence of longitudinal splits result in the reduction of stress concentration effects near fibe fractures. This results in a global strain controlled failure in the 810 O system. It is concluded that the presence of different fiber sizings result in different damage modes and failure mechanisms in the cross-ply laminates used in this study.Research Associate, Research Assistant, Alexander Giacco Professor and Professor respectively.     

Damage development in carbon/epoxy laminates under quasi-static and dynamic loading

The contrasting characteristics of damage evolution have been examined in a multidirectional carbon/epoxy composite laminate (IM7/8551-7) subjected to both quasi-static and dynamic loading. Our experiments were performed on bend-test bars that were loaded either in ‘supported' four-point bending or under ‘unsupported' conditions with a Hopkinson pressure bar to induce dynamic loading. We found differences in the damage that occurred in specimens loaded by the two techniques, in terms of the number of cracks and the length of the cracks. In the case of quasi-static loading, there were many matrix cracks within individual plies and only a few delamination cracks between plies; the maximum ratio of numbers of matrix to delamination cracks observed was 6:1. Despite their small number, the delamination cracks had a greater total length than the matrix cracks, and specimen failure occurred as a result of delamination crack propagation. During dynamic loading, the ratio between numbers of matrix and delamination cracks was 3:1, and in this case the ratio between the total crack lengths was unity. A quantitative assessment of damage induced during quasi-static bending was made from specimen stiffness results. Using simple beam theory and knowing the location of the damage, we correlated beam stiffness to the materials effective elastic modulus. We found that the composite's effective modulus decreased rapidly with small amounts of initial damage, but that subsequent increases in damage decreased the effective modulus at a much lower rate.     

Multiaxial fatigue and failure analysis of helical compression springs

Multiaxial fatigue criteria are applied to the analysis of helical compression springs. The critical plane approaches, Fatemi–Socie and Wang–Brown, and the Coffin–Manson method based on shear deformation, were used to predict fatigue lives of the springs under constant amplitude loading. Experimental fatigue lives are compared with the multiaxial fatigue criteria predictions. The stress analysis was carried out in the finite element code ANSYS, and the multiaxial fatigue study was performed using the fatigue software nCode. A failure analysis was conducted in order to determine the fatigue crack initiation point and a comparison of that location with the most damaged zone predicted by the numerical analysis is made. The Fatemi–Socie critical plane approach gives a good prediction of fatigue life. While the Wang–Brown criterion overestimates spring fatigue life, the Coffin–Mason model gives conservative results.     

Fatigue characterization and modeling of 30CrNiMo8HH under multiaxial loading

Fatigue of 30CrNiMo8HH steel alloy has been studied thoroughly. Uniaxial cyclic tension-compression, cyclic torsion, proportional tension-torsion, and non-proportional tension-torsion at various strain ratios have been considered. Tests were performed at standard laboratory conditions on solid and tubular specimens machined from an actual driveline component. Fractography was conducted on the tested samples to investigate the fatigue mechanisms involved. Under torsion, large numbers of early micro cracks were found to emanate from the sample's surface, with a few propagating into very long longitudinal cracks. In biaxial tests, cracks tend to propagate into the gauge reducing the cross section area. A strain energy density fatigue parameter has been employed for life prediction of the material under uniaxial and biaxial loading. The life prediction method is based on two different cracking mechanisms that agree with the observed cracking mechanisms in torsion and biaxial loading of 30CrNiMo8HH steel alloy studied here. Energy-based properties are obtained and the predicted lives are compared to experimental results. The results obtained agree well with experiments.     

Experimental study on mechanical behavior of brittle marble samples containing different flaws under uniaxial compression

Uniaxial compression experiments were carried out for the marble samples (located in the eastern ground of China) with different pre-existing flaws in non-overlapping geometry by the rock mechanics servo-controlled testing system. Based on the experimental results of complete axial stress-axial strain curves, the effect of flaw geometry on the strength and deformation behavior of marble samples is made a detailed analysis. Compared with the intact marble sample, the marble samples with different pre-existing flaws show the localization deformation failure. The uniaxial compressive strength (UCS), elastic modulus and peak axial strain of marble samples with pre-existing flaws are all lower than that of intact marble sample, and the reduction extent is closely related to the geometry of pre-existing flaws. The crack coalescence were observed and characterized from internal tips of different pre-existing flaws in brittle marble sample. Eight different crack types were identified based on their geometry and crack propagation mechanism (tensile, shear and compressive) for two pre-existing flaws, which can be used to analyze the failure mode and cracking process of marble sample containing different flaws in uniaxial compression. In the end, the influence of the crack coalescence on the strength and deformation failure behavior of brittle marble sample is analyzed under uniaxial compression. The present research provides increased understanding of the fundamental nature of rock failure under uniaxial compression.     

一维动静组合加载下深部石英片岩破坏研究

为研究锡铁山铅锌矿深部石英片岩的力学特性,利用分离式霍普金森杆(SHPB)对埋深863¹ 264m的试样进行25、30、35MPa轴压下的一维动静加载实验,和采用LS-DYNA软件模拟了25、30、35、40、45、50 MPa轴压情况下的冲击实验。研究结果表明:在冲击作用下,试样的一维动态抗压强度和破坏所需的入射能随着埋深的增加而增加,并呈现出常见的压剪破坏模式;当轴压40MPa左右,埋深1 428m的岩石动态抗压值达到最大;当轴压低于40 MPa时,轴压的增大能加强试样的抗压能力;当轴压大于40MPa时,轴压的增加反而减弱了试样的抗压能力。     

Investigation of combined stress state failure criterion for glass fiber/epoxy interface by the cruciform specimen method

The interfacial failure criterion under combined stress state in a glass fiber/epoxy composite is investigated by the cruciform specimen method. Experiments were conducted by using specimens with a fiber whose angle from the loading direction is varied in order to make various stress state of normal and shear at the interface. Finite element analysis is performed to calculate the interfacial stress distribution. By combining the experimental measurement of the specimen stress at the interfacial debonding initiation and the finite element stress analysis, it is possible to obtain the interfacial stress state at interfacial failure. A method to determine the interfacial failure criterion and the interfacial failure initiation location simultaneously is proposed in the present study. We conclude the value of the interfacial shear strength is higher than that of the interfacial normal strength for the material system used in the present study.     

Postbuckling response and failure of symmetric laminates under in-plane shear

This paper summarizes a study aimed at understanding the postbuckling behaviour and progressive failure of thin, simply supported symmetric rectangular laminates with various possible in-plane boundary conditions and under the action of in-plane shear loads. First-order shear deformation theory and geometric non-linearity, in the von-Karman sense, is used with a finite-element procedure. The 3D Tsai–Hill criterion is used to predict failure of lamina and the maximum stress criterion is used to predict the onset of delamination at the interface of two adjacent layers. The effect of in-plane boundary conditions, plate lay-ups, plate aspect ratio, fiber orientations and lamina material properties on the load deflection response, buckling load, first-ply failure load, ultimate load and the maximum transverse displacement associated with failure loads is presented.     

Role of matrix modification on interlaminar shear strength of glass fibre/epoxy composites

Interlaminar shear properties of fibre reinforced polymer composites are important in many structural applications. Matrix modification is an effective way to improve the composite interlaminar shear properties. In this paper, diglycidyl ether of bisphenol-F/diethyl toluene diamine system is used as the starting epoxy matrix. Multi-walled carbon nanotubes (MWCNTs) and reactive aliphatic diluent named n-butyl glycidyl ether (BGE) are employed to modify the epoxy matrix. Unmodified and modified epoxy resins are used for fabricating glass fibre reinforced composites by a hot-press process. The interlaminar shear strength (ILSS) of the glass fibre reinforced composites is investigated and the results indicate that introduction of MWCNT and BGE obviously enhances the ILSS. In particular, the simultaneous addition of 0.5 wt.% MWCNTs and 10 phr BGE leads to the 25.4% increase in the ILSS for the glass fibre reinforced composite. The fracture surfaces of the fibre reinforced composites are examined by scanning electron microscopy and the micrographs are employed to explain the ILSS results.