A failure criterion for brittle elastic materials under mixed-mode loading

The failure criterion of Leguillon at reentrant corners in brittle elastic materials (Leguillon 2002, Eur J Mech A/Solids 21: 61–72; Leguillon et al. (2003), Eur J Mech A—Solids 22(4): 509–524) validated in (Yosibash et al. 2004, Int J Fract 125(3–4): 307–333) for mode I loading is being extended to mixed mode loading and is being validated by experimental observations. We present an explicit derivation of all quantities involved in the computation of the failure criterion. The failure criterion is validated by predicting the critical load and crack initiation angle of specimens under mixed mode loading and comparison to experimental observations on PMMA (polymer) and Macor (ceramic) V-notched specimens.     

A numerical study of fracture initiation in a ductile material containing a dual population of second-phase particles—II. Dynamic loading

Some recent experimental studies with pre-notched bend specimens of 4340 steel under both static loading [A. T. Zehnder and A. J. Rosakis, J. appl. Mech. 57, 618–626 (1990)] and impact loading [A. T. Zehnder et al., Int. J. Fracture 42, 209–230 (1990)] have shown that considerable crack-tunneling occurs in the interior of the specimens prior to gross fracture initiation on the free surfaces. The final fracture of the side ligaments happens because of shear-lip formation. The tunneled region is characterized by a flat fibrous fracture surface. In Part I of this work, the static experiments of A. T. Zehnder and A. J. Rosakis [J. appl. Mech. 57, 618–626 (1990)] were analyzed using a 2D plane-strain finite-element procedure. The constitutive model that was employed in this analysis accounted for the ductile failure mechanisms of microvoid nucleation, growth and coalescence. The simulation also modeled void initiation at two populations of particles of different sizes. In this part, the same constitutive model as in Part I is used, along with a plane-strain transient finite-element procedure to analyze the impact experiments reported by A. T. Zehnder et al., [Int. J. Fracture 42, 209–230 (1990)] corresponding to an impact speed of 5 m/sec. A direct comparison is made between the static and dynamic results regarding the development of ductile failure in the ligament connecting the notch-tip and a simulated inclusion ahead of it. It is found that, to attain the same level of microvoid damage in this ligament, a larger value of J is required under dynamic loading. The strain rate and adiabatic temperature rise near the notch-tip are also examined.     

A numerical study of fracture initiation in a ductile material containing a dual population of second-phase particles—I. Static loading

Some recent experimental studies with pre-notched bend specimens of 4340 steel under both static loading [A. T. Zehnder and A. J. Rosakis, J. appl. Mech. 57, 618–626 (1990)] and impact loading [A. T. Zehnder et al., Int. J. Fracture 42, 209–230 (1990)] have shown that considerable crack tunneling occurs in the interior of the specimens prior to gross fracture initiation on the free surfaces. The final fracture of the side ligaments happens because of shear lip formation. The tunneled region is characterized by a flat fibrous fracture surface. In this work, the above experiments are analyzed using a 2D plane-strain finite-element procedure which is expected to simulate local material failure in the center-plane of the 3D specimen accurately. The rate-independent version of the Gurson model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. Two populations of second-phase particles are considered, including large inclusions which initiate voids at an early stage, and small particles which require large strains to nucleate voids. Attention is focused on the formation of a discrete void around a simulated inclusion ahead of the notch-tip, its growth and link-up with the notch-tip via a sheet of microvoids. In Part I of the work, the results obtained from the finite-element analysis of the static fracture initiation test [A. T. Zehnder and A. J. Rosakis, J. appl. Mech. 57, 618–626 (1990)] are presented. It is found that the value of the J-integral at which material failure near the notch-tip commences in the present simulation agrees well with experimental observations regarding the onset of crack tunneling. The analysis of the impact fracture test of [A. T. Zehnder et al., Int. J. Fracture 42, 209–230 (1990)] will be taken up in Part II.     

Modeling and characterization of dynamic failure of borosilicate glass under compression/shear loading

In this paper, we study the impact-induced dynamic failure of a borosilicate glass block using an integrated experimental/analytical approach. Previous experimental studies on dynamic failure of borosilicate glass have been reported by Nie et al. [Nie X, Chen WW, Sun X, Templeton DW. Dynamic failure of borosilicate glass under compression/shear loading – experiments. J Am Ceram Soc, in press.] using the split Hopkinson pressure bar (SHPB) technique. The damage growth patterns and stress histories have been reported for various glass specimen designs. In this study, we propose to use a continuum damage mechanics (CDM)-based constitutive model to describe the initial failure and subsequent stiffness reduction of glass. Explicit finite element analyses are used to simulate the glass specimen impact event. A maximum shear stress-based damage evolution law is used in describing the glass damage process under combined compression/shear loading. The impact test results are used in quantifying the critical shear stress for the borosilicate glass under examination. It is shown that with only two modeling parameters, reasonably good comparisons between the predicted and the experimentally measured failure maps can be obtained for various glass sample geometries. Comparisons between the predicted stress histories for different sample designs are also used as model validations.     

Introduction of damage evolution in a scale transition approach for highly-filled particulate composites

The present paper deals with a non-conventional scale transition for modelling the behaviour of highly-filled particulate composites, starting from a methodology initially proposed by Christoffersen [Christoffersen J. Bonded granulates. J Mech Phys Solids 1983;31:55–83] and recently extended by Nadot et al. [Nadot C, Dragon A, Trumel H, Fanget A. Damage modelling framework for viscoelastic particulate composites via a scale transition approach. J Theor Appl Mech 2006;44(3):553–83] in presence of damage. The model thus obtained is here completed with several ingredients allowing to describe damage evolution and in particular a defect nucleation criterion as well as a closure criterion. These criteria are formulated in terms of displacement, and so as to ensure continuity in terms of macroscopic stress. They are finally introduced in an iterative numerical solving procedure which allows to follow damage evolution as a discrete sequence of interfacial debonding including also eventual closure of defects.     

Analysis of a delayed fracture criterion for lifetime prediction of viscoelastic polymer materials

In this work a multi-axial yield/failure model for viscoelastic/plastic materials is applied, which was developed by Naghdi and Murch (in J.?Appl. Mech. 30:321?C328, 1963) and later extended and refined by Crochet (in J.?Appl. Mech. 33:327?C334, 1966), to predict long-term creep rupture of polymers. The criterion defines a function, which depends on time, the viscoelastic properties and applied stress, to establish an empirical law with creep yield (fracture). In this work a linear relationship is proposed, defined as a time-dependent failure criterion, which can be applied for extrapolation purposes. A comparative analysis using energy-based failure criteria is performed. It is proved, for the polymers considered in this study, that the proposed time-dependent failure criterion holds for long times. Experimental data are used to illustrate the applicability of this time-dependent failure criterion.     

Multi-surface failure criterion for saline ice in the brittle regime

In this paper, the development of a 3-D failure criterion for saline ice is presented. The need for such general 3-D failure formulation stems from the fact that, during ice–ship interactions, ice undergoes a complex state of deformation and stress before it fails and breaks away, and the use of the uniaxial strength of ice to compute impact ice loads may lead to inaccurate load calculations and non-conclusive results.In recent years, with the availability of High Power Computers (HPC), numerical methods are being used more than ever before in marine and ice engineering problems. Numerical models based on computational techniques such as finite elements, boundary elements and discrete elements require 3-D constitutive models and failure criteria to represent the behavior of the materials involved (such as the behavior of the ship structure, ice and water “fluid”).At high-speed impacts (strain rates >10⁻³ s⁻¹), ice behaves as a linear elastic material with a brittle mode of failure. Previously, Derradji-Aouat [Derradji-Aouat, A., 2000. A unified failure envelope for isotropic freshwater ice and iceberg ice. ASME/OMAE-2000, Int. Conference on Offshore Mechanics and Arctic Engineering, Polar and Arctic section, New Orleans, US, PDF file # OMAE-2000-P/A # 1002] developed a unified 3-D failure envelope for both fresh water isotropic ice and iceberg ice. In this paper, that formulation is extended to include failure of saline ice (in addition to fresh water ice and iceberg ice). The results of a significant number of true triaxial tests using Laboratory Grown Ice (LGSI) were obtained from the open literature. The results of these tests formed a database that enables the existing failure model [Derradji-Aouat, A., 2000. A unified failure envelope for isotropic freshwater ice and iceberg ice. ASME/OMAE-2000, Int. Conference on Offshore Mechanics and Arctic Engineering, Polar and Arctic section, New Orleans, US, PDF file # OMAE-2000-P/A # 1002] to be extended from the isotropic fresh water ice and iceberg ice to columnar saline ice.Mroz's [J. Mech. Phys. Solids 15 (1967) 163] concept for the multi-surface failure theory is used in both studies (the present study, for saline ice, as well as in the previous study, for the fresh water isotropic ice and iceberg ice). It appears that the same set of the equations is applicable to the failure of all three types of ice. The possibility of the existence of a universal and general failure criterion for all types of ice is discussed.The validation of the present multi-surface failure criterion was discussed on the basis of comparisons between predicted failure curves and actual true triaxial test results. An overall discrepancy of predicted versus measured strength values of less than 20% was calculated.     

A criterion for brittle fracture in U-notched components under mixed mode loading

A failure criterion is proposed for brittle fracture in U-notched components under mixed-mode static loading. The criterion, called UMTS, is developed based on the maximum tangential stress criterion and also a criterion proposed in the past for mode I failure of rounded V-shaped notches [Gomez FJ, Elices M. A fracture criterion for blunted V-notched samples. Int J Fracture 2004;127:239-64]. Using the UMTS criterion, a set of fracture curves are derived in terms of the notch stress intensity factors. These curves can be used to predict the mixed mode fracture toughness and the crack initiation angle at the notch tip. An expression is also obtained from this criterion for predicting fracture toughness of U-notched components in pure mode II loading. It is shown that there is a good agreement between the results of UMTS criterion and the experimental data obtained by other authors from three-point bend specimens.     

Progressive damage modeling in fiber-reinforced materials

This paper presents an anisotropic damage model suitable for predicting failure and post-failure behavior in fiber-reinforced materials. In the model the plane stress formulation is used and the response of the undamaged material is assumed to be linearly elastic. The model is intended to predict behavior of elastic-brittle materials that show no significant plastic deformation before failure. Four different failure modes – fiber tension, fiber compression, matrix tension, and matrix compression – are considered and modeled separately. The onset of damage is predicted using Hashin’s initiation criteria [Hashin Z, Rotem A. A fatigue failure criterion for fiber-reinforced materials. J Compos Mater 1973;7:448; Hashin Z. Failure criteria for unidirectional fiber composites. J Appl Mech 1980;47:329–34] and the progression of damage is controlled by a new damage evolution law, which is easy to implement in a finite element code. The evolution law is based on fracture energy dissipation during the damage process and the increase in damage is controlled by equivalent displacements. The issues related to numerical implementation, such as mesh sensitivity and convergence in the softening regime, are also addressed.     

Uncertain dynamic response of a deterministic elastic–plastic beam

The counterintuitive phenomenon of elastic–plastic beam dynamics was demonstrated by Symonds and Yu (ASME J Appl Mech 1985;52:517). An analytical model has been developed to explain this phenomenon from a deterministic viewpoint. However, experimental evidence in (Int J Impact Eng 1991;11(3):341; Int J Impact Eng 1991;11(4):445) showed that the response of this deterministic system is uncertain, which is studied qualitatively in the present paper based on parametric sensitive characteristics of the deterministic system and parametric uncertainty of the studied system. FEM and Monte Carlo method are applied to study this phenomenon.     

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.     

Comments on “Is the cause of size effect on structural strength fractal or energetic-statistical?” by Ba?ant & Yavari [Engng Fract Mech 2005;72:1-31]

Aim of this letter to the Editor is at replying to the criticisms raised by Ba?ant and Yavari [Ba?ant ZP, Yavari A. Is the cause of size effect on structural strength fractal or energetic - statistical? Engng Fract Mech 2005;72:1-31] against the fractal approach to the size-scale effects on the mechanical properties of materials and the concept of the Multi-Fractal Scaling Law presented by Carpinteri [Carpinteri A. Scaling laws and renormalization groups for strength and toughness of disordered materials. Int J Solids Struct 1994;31:291-302]. These criticisms will be analysed thoroughly, showing how they also contain some mistakes and misunderstandings. The presented elucidations should redirect the discussion to a more correct scientific debate.     

Condensation of refrigerants in horizontal microfin tubes: comparison of prediction methods for heat transfer

A comparison was made between the predictions of previously proposed empirical correlations and theoretical model and available experimental data for the heat transfer coefficient during condensation of refrigerants in horizontal microfin tubes. The refrigerants tested were R11, R123, R134a, R22 and R410A. Experimental data for six tubes with the tube inside diameter at fin root of 6.49–8.88 mm, the fin height of 0.16–0.24 mm, fin pitch of 0.34–0.53 mm and helix angle of groove of 12–20° were adopted. The r.m.s. error of the predictions for all tubes and all refrigerants decreased in the order of the correlations proposed by Luu and Bergles [ASHRAE Trans. 86 (1980) 293], Cavallini et al. [Cavallini A, Doretti L, Klammsteiner N, Longo L G, Rossetto L. Condensation of new refrigerants inside smooth and enhanced tubes. In: Proc. 19th Int. Cong. Refrigeration, vol. IV, Hague, The Netherlands, 1995. p. 105–14], Shikazono et al. [Trans. Jap. Sco. Mech. Engrs. 64 (1995) 196], Kedzierski and Goncalves [J. Enhanced Heat Transfer 6 (1999) 16], Yu and Koyama [Yu J, Koyama S. Condensation heat transfer of pure refrigerants in microfin tubes. In: Proc. Int. Refrigeration Conference at Purdue Univ., West Lafayette, USA, 1998. p. 325–30], and the theoretical model proposed by Wang et al. [Int. J. Heat Mass Transfer 45 (2002) 1513].     

Stress-strain relations in elastoplastic solids with Dugdale-type cracks

Mechanical behavior of a two-dimensional elastoplastic solid with rectilinear cracks is investigated. Plastic strip model is used to reduce plasticity problem to the equivalent linear elasticity formulation. Two realizations of the mixed mode plastic strip model are considered: in-line plastic strips as proposed by Becker and Gross [Int. J. Fract. 37 (1988) 163], and inclined plastic strips of Panasyuk and Savruk [Appl. Mech. Rev. 47 (1994) 151]. The effective mechanical response predictions are based on the procedure presented in Kachanov et al., [Appl. Mech. Rev. 47 (1994) 151]. Stress-strain relations are obtained for parallel and randomly oriented non-interacting cracks. Results are compared with known elastic solutions.     

A probabilistic model for cleavage fracture with a length scale - Parameter estimation and predictions of growing crack experiments

A probabilistic model for the cumulative probability of failure by cleavage fracture was applied to experimental results where cleavage fracture was preceded by ductile crack growth. The model, introduced by Kroon and Faleskog [Kroon M, Faleskog J. A probabilistic model for cleavage fracture with a length scale - influence of material parameters and constraint. Int J Fract 2002;118:99-118], includes a non-local stress with an associated material related length scale, and it also includes a strain measure to account for the number of nucleated cleavage initiation sites. The experiments were performed on single edge cracked bend test specimens with three different crack lengths at the temperature 85 °C, which is in the upper transition region for the steel in question. The ductile rupture process is modelled using the cell model for nonlinear fracture mechanics. The original cleavage fracture model had to be modified in order to account for the substantial number of cleavage initiators being consumed by the ductile process. With this modification, the model was able to accurately capture the experimental failure probability distribution.     

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

In Anderson Jr CE, Orphal DL, Behner T, Templeton, DW [Failure and penetration response of borosilicate glass during short-rod impact. Int J Impact Eng 2009, doi:10.1016/ j.ijimpeng.2008.12.002.] it was demonstrated that the failure front (FF) produced by the penetration of a borosilicate glass target by a gold rod ceased to propagate a short time after the rod was fully eroded. This strongly suggests that progression of the FF is not described by a wave equation. Here it is shown that propagation of the FF is reinitiated if a second co-axial rod, spaced a distance from the first, impacts the glass at the bottom of the penetration channel. The experiments were performed in reverse ballistic mode with two short rods spaced apart. In some experiments both rods were gold; in other experiments, one rod was copper and the other gold. FF propagation was measured using high-speed photography; rod penetration was measured using multiple, independent flash X-rays. Much of the observed phenomenology can be modeled assuming that the rod, either first or second, “communicates” with the FF at a speed corresponding to the bulk sound speed of the undamaged glass.     

Prediction of ductile failure using a local strain-to-failure criterion

In this article, we provide the details of the predictive simulations performed by the University of Texas team in response to the 2012 Sandia Fracture Challenge (Boyce et al. in The Sandia Fracture challenge: blind predictions of ductile tearing. Int J Fract. doi:10.1007/10704-013-9904-6, 2013). The material constitutive model was calibrated using the tensile test data through an optimization scheme. A modified Johnson–Cook failure criterion was also partially calibrated using the material characterization data obtained from a tension test and a compact-tension fracture test. These models are then embedded in a highly refined finite element simulation to perform a blind prediction of the failure behavior of the Sandia Fracture Challenge geometry. These results are compared with experiments performed by Sandia National Laboratories and additional experiments that were performed at the University of Texas at Austin with full-field three-dimensional digital image correlation in order to explore the different failure modes. It is demonstrated that a well-calibrated model that captures the essential elastic–plastic constitutive behavior is necessary to confidently capture the elasto-plastic response of challenging structural geometries; it is also shown that a simple ductile failure model can be used to predict ductile failure correctly, when proper calibration of the material model is established.     

Further remarks on persistence of straining and flow classification

We revisit the kinematic flow classification developed in Thompson and Souza Mendes (2005) [R.L. Thompson, P.R. de Souza Mendes, Persistence of straining and flow classification, Int. J. Engng. Sci. 43 (1–2) (2005) 79–105] and give an improved physical interpretation to the persistence-of-straining tensor. The criterion is, then, applied to an intrinsically unsteady viscometric flow proposed by Yin and Pipkin (1970) [W.L. Yin, A.C. Pipkin, Kinematics of viscometric flow, Arch. Rational Mech. Anal. 37 (1970) 111–135].     

CTH simulations of an expanding ring to study fragmentation

A high velocity impact will result in fragmentation which can be seen through EO/IR/RF signatures. Understanding fragmentation and how it relates to signatures is key to being able to characterize the impact. To study fragmentation in a computational context, an expanding ring was simulated using the shock physics hydrocode CTH. The simulations were set up to approximate the conditions of experiments performed by Zhang and Ravi-Chandar [On the dynamics of necking and fragmentation – I. Real-time and post-mortem observations in Al 6061-O. Int J Fract 2006;142:183–217]. The simulations resulted in random fragmentation patterns that are mesh size dependent. The simulations could not capture either the fragment sizes and distributions or the physics of the failure mechanism seen in experiments. The mechanics of failure represented in the simulations is extremely sensitive to the material model and how damage is treated in that model. However, the average fragment size in the simulations versus strain rate was found to be consistent with popular fragmentation models such as Grady–Kipp and Zhou–Molinari–Ramesh.