Element-failure concepts for dynamic fracture and delamination in low-velocity impact of composites

An element-failure algorithm is proposed and incorporated into a finite element code for simulating dynamic crack propagation and impact damage in laminated composite materials. In this algorithm, when a crack is propagating within a finite element, the element is deemed to have partially failed, but not removed from the computations. Consequently, only a fraction of the stresses that were computed before the crack tip entered the element contribute to the nodal forces of the element. When the crack has propagated through the element, the element is completely failed and therefore can only resist volumetric compression. This treatment of crack propagation in isotropic solids allows fracture paths within individual elements and is able to accommodate crack growth in any arbitrary direction without the need for remeshing. However, this concept is especially powerful when extended to the modeling of damage and delamination in fibre-reinforced composite laminates. This is because the nature of damage in composite laminates is generally diffused, characterized by multiple matrix cracks, fibre pullout, fibre breakage and delaminations. It is usually not possible to define or identify crack tips in the tradition of fracture mechanics. Since parts of a damaged composite structure are often able to partially transmit load despite the presence of some damage, it is advantageous to model the damaged portions with partially failed elements. The damage may be efficiently modeled and tracked using element-failure concepts, with the application of appropriate failure criteria and damage evolution laws. The idea is to embody the effects of damage into the effective nodal forces of the finite element. In this paper, we report the novel use of element-failure concepts in the analysis of low-velocity impact damage of composite laminates. The initiation and propagation of delaminations arising from the impact are predicted and the results show qualitative agreement with experimental observation of the formation of multiple delaminations in impact-damaged specimens. While such delaminations do not permit transmission of tensile stress waves across the cracked surfaces, transmission of compressive stress waves are allowed in the simulation. It is further shown that, when elements are allowed to fail, the dynamic stress wave distributions are altered significantly. In the element-failure algorithm, the issue of interpenetration of delamination surfaces in the model does not arise. This is a significant advantage over the conventional method of explicitly modeling the delamination surfaces and crack front, where generally, much computational time must be spent in employing contact algorithms to ensure physically admissible solutions. Finally, we also demonstrate the simulation of crack propagation of pre-notched specimens of an isotropic material under initial conditions of mode II loading using the element-failure algorithm. The numerical results showed that the cracks propagated at an angle of about 70° with respect to the notches, in agreement with the experimental results of Kalthoff.     

Low strain rate testing based on drop weight impact tester

Experimental Techniques - As the use of fiber composites extends to automotive applications, there is a need to characterize the composite properties at low strain rates, such as below 100/s. In...     

SHPB冲击加载下四种岩石的复合型动态断裂实验研究

分别用绿砂岩、黄砂岩、灰砂岩、大理岩制作了三种几何相似的(φ80mm、φ122mm、φ155mm)中心直裂纹平台巴西圆盘(CSTFBD)试样;利用分离式霍普金森压杆加载,进行了I型和I-II型复合动态断裂实验,并由实验结合有限元分析得到了四种岩石材料的I、II型动态断裂韧度KId、KIId。研究表明:动态断裂韧度均存在尺寸效应,试样尺寸对I-II型复合比和纯II型加载角均会产生影响,复合比随尺寸的增大而减小,大尺寸试样II型加载的加载角比小尺寸试样的小。同时,由于负值的T应力显著减小了裂纹的起裂角,用广义最大拉应力准则预测的起裂角更符合实验结果。     

Effects of non-uniform strains on tensile fracture of fiber-reinforced ceramic composites

Effects of non-uniform strains on tensile fracture of fiber-reinforced ceramic–matrix composites have not been satisfactorily explained by existing mechanics-based models. In this paper, we use an exact model of fiber fragmentation under global load sharing conditions to predict fracture in three model problems in which non-uniform strains occur: (i) an end-constrained plate subject to a linear transverse temperature gradient; (ii) an internally-pressurized cylindrical tube with a linear through-thickness temperature gradient; and (iii) a rectangular beam under combined bending and tension. Fracture is assumed to occur when the global load reaches a maximum value. Approximations to the exact fragmentation model are also assessed, with the goal of decoupling the effects of two important parts of the computed stress–strain response: the rate of post-peak strain softening and the magnitude of the plateau “flow” stress once fiber fragmentation is complete. We find that for cases in which the fiber Weibull modulus is low and hence its plateau strength is high relative to its peak and the loading yields a sufficiently high strain gradient, the failure strain lies in the plateau regime. Consequently, the results can be predicted with good accuracy using a perfectly-plastic representation of the post-peak response. In contrast, for cases in which the fiber Weibull modulus is high, the failure strain lies in the softening portion of the curve. Here a linear-softening model is found to yield accurate results. A preliminary assessment of the model has been made by comparing predicted and measured bending/tension strength and failure strain ratios for one specific composite. The correlations appear good, though additional experiments are required in order to critically assess the model predictions over a range of loading scenarios.     

Search for conditions of compressive fracture of hard brittle ceramics at impact loading

In this paper we discuss three different experimental configurations to diagnosing the modes of inelastic deformation and to evaluating the failure thresholds at shock compression of hard brittle solids. One of the manifestations of brittle material response is the failure wave phenomenon, which has been previously observed in shock-compressed glasses. However, based on the measurements from our “theory critical” experiments, both alumina and boron carbide did not exhibit this phenomenon. In experiments with free and pre-stressed ceramics, while the Hugoniot elastic limit (HEL) in high-density B₄C ceramic was found to be very sensitive to the transverse stress, it was found relatively less sensitive in Al₂O₃, implying brittle response of the boron carbide and ductile behavior of alumina. To further investigate the effects of stress states on the shock response of brittle materials, a “divergent flow or spherical shock wave” based plate impact experimental technique was employed to vary the ratio of longitudinal and transversal stresses and to probe conditions for compressive fracture thresholds. Two different experimental approaches were considered to generate both longitudinal and shear waves in the target through the impact of convex flyer plates. In the ceramic target plates, the shear wave separates a region of highly divergent flow behind the decaying spherical longitudinal shock wave and a region of low-divergent flow. Experiments with divergent shock loading of alumina and boron carbide ceramic plates coupled with computer simulations demonstrated the validity of these experimental approaches to develop a better understanding of fracture phenomena.     

A direct-tension split Hopkinson bar for high strain-rate testing

A direct-tension split-Hopkinson-bar apparatus is introduced. In this apparatus the specimen is loaded by a tensile wave that is generated by the release of a stored load in a section of the input bar. The system can be used for experiments with test durations of up to 500 s. The effect of specimen geometry (length to diameter ratio) is investigated. Consistent results are obtained when the ratio is larger than about 1.60. Results from tests with 6061-T651 aluminum are in agreement with published data.Paper was presented at the 1990 SEM Spring Conference on Experimental Mechanics held in Albuquerque, NM on June 3–6.     

A modified torsional kolsky bar for investigating dynamic friction

This paper introduces an experiment to investigate dry sliding resistance of frictional interfaces at normal pressures up to 100 MPa, slip speeds up to 10 m/s and slip distances of approximately 10 mm. This new apparatus involves a novel modification of the conventional torsional Kolsky bar apparatus, employed extensively in the past for investigating high strain rate behavior of engineering materials. The new experimental configuration represents a significant improvement over conventional tribology experiments because it uses elastic torsional waves with a superimposed static compressive force to control the interfacial traction. Moreover, the apparatus allows critical frictional parameters such as the interfacial sliding resistance, slip speeds and slip without the use of transducers at the frictional interface. The usefulness of the device is demonstrated by presenting results of high-speed friction on 6061-T6 Al/1018 steel and Carpenter Hampden tool steel/7075-T6 Al tribo pairs.     

A numerical study on the deformation and fracture modes of steel projectiles during Taylor bar impact tests

A heterogeneous material model based on macro-mechanical observations is proposed for simulation of fracture in steel projectiles during impact. A previous experimental study on the deformation and fracture of steel projectiles during Taylor bar impact tests resulted in a variety of failure modes. The accompanying material investigation showed that the materials used in the impact tests were heterogeneous on scales ranging from microstructure as investigated with SEM to variation in fracture strains from tensile tests. A normal distribution is employed to achieve a heterogeneous numerical model with respect to the fracture properties. The proposed material model is calibrated based on the tensile tests, and then used to independently simulate the Taylor bar impact tests. A preliminary investigation showed that the simulations are sensitive to assumptions regarding the anvil behaviour and friction properties. A flexible anvil and a yield-limited friction law are shown to be necessary to correctly reproduce the experimental behaviour. The proposed model is then shown to be capable of correctly reproducing all fracture modes but one, and also predict critical impact velocities for projectile fracture with reasonable accuracy. Fragmentation at velocities above the critical velocity is not well reproduced due to excessive element erosion. Measures to make the element erosion process more physical are proposed and discussed with their respective drawbacks. The use of a simple fracture criterion in combination with an element erosion technique accentuates the effect of distributing the fracture parameter.     

A machine for static and dynamic triaxial testing

A machine has been developed for studying the static and dynamic triaxial constitutive behavior of large specimens of geologic and construction materials. Test specimens can also contain a cylindrical tunnel cavity to permit study of tunnel-reinforcement structures and rock-structure interaction. The specimens are 0.3 m in diameter and 0.3 to 0.45 m high; the model tunnels can be up to 50 mm in diameter. Static and dynamic triaxial loads can be applied with maximum pressures of 200 MPa in static tests and 100 MPa in dynamic tests. Dynamic loading can also be superimposed on a static preload as large as 20 MPa. To facilitate study of tunnel reinforcement, the tunnel is maintained at ambient pressure, with access at both ends for instrumentation and photography. Example results show the influence on tunnel deformation of loading rate as well as the presence of joints and their orientation. For a given allowable tunnel closure, substantially greater pressures can be sustained under dynamic loading than under static loading, and substantially greater pressures can be sustained by an intact specimen than by a jointed specimen.     

Virtual testing applied to transverse multiple cracking of tows in woven ceramic composites

The present paper proposes a method of virtual testing with a view to investigating the local response of tows within textile ceramic matrix composite (CMC) under various loading conditions. The method was developed on 2D woven SiC/SiC composites. It capitalizes on knowledge on mechanical damage phenomenology and data established in previous works. It is applied to isolated transverse tows subjected to uniaxial loading by parallel longitudinal tows. The transverse tows contain heterogeneities like matrix voids, fibres and interphases. Mesh for finite element analysis is constructed from micrographs of composite cross section. Cracks were introduced into the mesh for simulation of multiple cracking. Transverse tow tensile behavior and data on distributions of flaw populations were derived from finite element computations of stress-state. Results were compared to experimental observations.     

Virtual testing applied to transverse multiple cracking of tows in woven ceramic composites

The present paper proposes a method of virtual testing with a view to investigating the local response of tows within textile ceramic matrix composite (CMC) under various loading conditions. The method was developed on 2D woven SiC/SiC composites. It capitalizes on knowledge on mechanical damage phenomenology and data established in previous works. It is applied to isolated transverse tows subjected to uniaxial loading by parallel longitudinal tows. The transverse tows contain heterogeneities like matrix voids, fibres and interphases. Mesh for finite element analysis is constructed from micrographs of composite cross section. Cracks were introduced into the mesh for simulation of multiple cracking. Transverse tow tensile behavior and data on distributions of flaw populations were derived from finite element computations of stress-state. Results were compared to experimental observations.     

Mesoscale modeling of nonlinear elasticity and fracture in ceramic polycrystals under dynamic shear and compression

Dynamic deformation and failure mechanisms in polycrystalline ceramics are investigated through constitutive modeling and numerical simulation. Two ceramics are studied: silicon carbide (SiC, hexagonal crystal structure) and aluminum oxynitride (AlON, cubic crystal structure). Three dimensional finite element simulations incorporate nonlinear anisotropic elasticity for behavior of single crystals within polycrystalline aggregates, cohesive zone models for intergranular fracture, and contact interactions among fractured interfaces. Boundary conditions considered include uniaxial strain compression, uniaxial stress compression, and shear with varying confinement, all at high loading rates. Results for both materials demonstrate shear-induced dilatation and increasing shear strength with increasing confining pressure. Failure statistics for unconfined loading exhibit a smaller Weibull modulus (corresponding to greater scatter in peak failure strength) in AlON than in SiC, likely a result of lower prescribed cohesive fracture strength and greater elastic anisotropy in the former. In both materials, the predicted Weibull modulus tends to decrease with an increasing number of grains contained in the simulated microstructure.     

A structural model of ceramics: Multiple fracture

The processes of deformation of ceramics containing multiple internal defects, and the dissemination of microcracks, are analyzed by considering an infinite periodic grid of underformable hexagonal grains connected with elastic bondings. The model of ceramics and the stress distribution at the vicinity of the local break, together with a discussion of the experimental data, were studied in the first part of the paper [1]. The model is based on the assumption that the strength of grains is higher than that of bondings, and the cracks in the material spread through the bondings. To calculate the stress state of the medium, a numerical method, based on Green's function and the superposition principle, is used. Defects, presented by failed bondings, are placed by polarization dipoles of forces and moments applied to the grains adjacent to the defect. The stress distributions in the perfect medium, loaded by the external loads and polarization dipoles, and in the medium, containing micro-cracking, should be the same. This condition allows us to obtain simultaneous linear equations in terms of polarization dipoles and to determine the stress state of the medium. The failure of bondings is characterized by the von Mises strength criterion. The results of numerical modeling of the origination of a microcrack from a system of defects, and its dissemination for various loading, are presented.

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Sommario Le modalita' di deformazione di materiali ceramici in presenza di difetti interni c la propagazione di microfratture sono analizzate considerando una griglia periodica di grani esagonali rigidi collegati tra loro mediante elementi elastici. Il modello di materiale ceramico, lo stato di sforzo in vicinanza di una frattura e la discussione di dati sperimentali sono stati presentati nella prima parte dell'articolo [1]. Il modello si basa sull'potesi che la rigidezza dei grani sia decisamente superiore a quella dei legami e chc le cricche si diffondano attraverso i legami medesimi. Per calcolare lo stato di sforzo si utilizza un metodo basato sulle funzioni di Green e sul principio di sovrapposizione. I difetti, rappresentati dai legami interrotti, sono rimpiazzati da dipoli di polarizzazione applicati ai grani adiacenti al difetto. Lo stato di sforzo nel materiale perfetto in presenza di carichi esterni e di dipoli, e nel materiale con microcricche sono considerali uguali. Questa condizione consente di ottenere un sistema linearc di equazioni in funzione di dipoli di polarizzazione e di determinare lo stato di sforzo. Il criterio di Mises e' utilizzato per individuare la rottura dei legami elastici. Vengono presentati, per diverse condizioni di carico, i risultati di simulazioni numeriche relative all'insorgere e alla propagazione di microfratture a partire da un'insieme di difetti.

     

A heuristic approach to microcracking and fracture for ceramics with statistical consideration

Microcracking damage and toughening are examined for ceramics. These effects have been found to depend on the material microstructure and macrocrack growth. Isotropic damage, attributed to random distribution of microcrack location, length and orientation can be associated with a disordered microstructure and a non-uniform residual stress field. When the applied stress is the main cause of cracking, the microcrack distribution is no longer random such as a system of quasi-parallel cracks. To highlight the effect of crack interaction, discrete models are advanced where damage is simulated by a distribution of microcracks. The dilute concentration assumption is invoked to simplify the analysis.The two-dimensional discrete model is based on a phenomenological approach that is statistical in character. Interactions of microcracks and with a macrocrack are considered by means of a boundary element technique (A. Brencich, A. Carpinteri, Int. J. Fracture 76 (1996) 373–389; A. Brencich, A. Carpinteri, Eng. Fract. Mech. 59 (1998) 797–814) where both isotropic and anisotropic damage could be treated. Comparisons with other results are made to show that the model can be applied to analyse the fracture behaviour of different materials.     

Damage analysis and fracture criteria for piezoelectric ceramics

Both the mechanical and the electrical damages are introduced to study fracture mechanics of piezoelectric ceramics in this paper. Two kinds of piezoelectric fracture criteria are proposed by using the damage theory combined with the well-known piezoelectric fracture experiments of Park and Sun [Fracture criteria of piezoelectric ceramics, J. Am. Ceram. Soc. 78 (1995) 1475-1480]. One is based on a critical state of the mechanical damage and the other on a critical value of a proper linear combination of both the mechanical and the electrical damage variables. It is found that the fracture load predicted, which takes the mechanical damage into account only (mode 1), has greater deviation than predicted result by considering a proper linear combination of the mechanical and the electrical damages (mode 2). And the fracture criterion corresponding to mode 2 presented is shown to be superior to mode 1. It is also demonstrated that the mechanical damage has greater effect on fracture than the electrical damage.     

A dynamic biaxial testing machine

The development of generalized constitutive equations for materials requires additional experimental data. A testing machine is described which is capable of applying biaxial, tension-torsion loading to thin-walled tubular specimens over a wide range in loading rates. Both components of the load are independently controlled. The objective is to obtain information on the effect of the rate of loading on viscoplastic or viscoelastic behavior of materials. Some preliminary data are given on the effect of loading rate on the yielding of mild steel. Paper was presented at 1966 SESA Spring Meeting held in Detroit, Mich., on May 4–6. The work presented herein was performed under Contract DA31-124-ARO-D-273 with the Army Research Office, Durham, Durham, N. C.     

Experimental testing of the fracture of concrete and reinforced concrete plates under impact

This paper describes the results of experimental studies on penetration of cylindrical projectiles into concrete and reinforced concrete at impact velocities reaching 0.5 km/s. An algorithm is proposed for calculating the depth of penetration of a projectile, making it possible to find the depth of penetration of high-strength steel projectiles with a mass of up to 13.5 kg into concrete on the basis of measurements of the specific work required to remove concrete using projectiles with a mass of up to 8 g.     

A simple testing technique for fracture under biaxial stresses

Evidence is accumulating to suggest that the fracture toughness of and cyclic crack-propagation rates in a material may be affected by stresses acting parallel to the crack plane. This effect contradicts the justifiable assumption, implicit in fracture-mechanics theory, that only loads causing a stress singularity at the tip of a crack can affect its behavior. More extensive investigation of this important problem involves the development of special testing equipment and specimens. This article offers a simple design for such a system, which has proved in practice to be highly reliable and of adequate accuracy. Preliminary tests on polymethylmethacrylate (PMMA) under biaxial fatigue and ramp loading are described, to demonstrate the technique itself and the phenomena under investigation. The results suggest that, for this material at least, the effects of transverse stresses are indeed slight.