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.     

Fatigue-fracture behavior of 5083-0 aluminum-magnesium alloy for LNG applications

Low temperature mechanical properties (including fatigue) of 5083-0 Al alloy are reviewed. Based on the results in the literature, the life of notched components under fatigue loaded conditon at LNG temperature (−162°C) are predicted. Probable reasons for low fatigue crack propagation life at low temperature are discussed. A procedure to theoretically generate the strain vs life plot is indicated. An elasto-plastic model presented by El-Haddad et al. [Int. J. Fracture 16, 15–30 (1980)] is used to study the effect of low temperature on J-integral values.     

A modified effective crack-length formulation in elastic-plastic fracture mechanics

In examining the performance of standard effective crack-length formulations, the authors noted quantitative accuracy up to “high” fractions of limit load under loading conditions for which the elastic T-stress was non-negative, while a pronounced deviation from the corresponding continuum elastic-plastic plane-strain finite-element solutions was seen in shallow-cracked geometries having negative T-stress. This trend can be rationalized by noting that, under modified boundary layer (K_I and T) loading, the maximum plastic zone radius strongly increases as the T-stress decreases from zero (J.R. Rice (1974), J. Mech. Phys. Solids 22, 17–26; S.G. Larsson and A.J. Carlsson (1973), J. Mech. Phys. Solids 21, 263–277; N.P. O'Dowd and C.F. Shih (1991), J. Mech. Phys. Solids 39(8), 989–1015.) Accordingly, we formulate a modified effective crack length to account for the effects of the elastic T-stress.

The new formulation consistently extends the load range for which accurate predictions of compliance, J-integral, and crack-tip constraint are obtained in several plane strain specimen geometries. The magnitude of influence of the T-stress varies with specimen type and relative crack depth. The greatest “improvement” to standard effective crack length approximations occurs in specimens of “moderately” negative T-stress.     

The effects of hyperbolic heat conduction around a dynamically propagating crack tip

Using infrared detectors, Zehnder and Rosakis (1991, J. Mech. Phys. Solids 39(3), 385), Zehnder and Kallivayalil (1991, SPIE ISS4A, 48) and Mason and Rosakis (1992, SN Report 92-2), have recorded the temperature field around a dynamically propagating crack tip travelling at constant velocity in several metals. At the same time, Tzou (1990a, J. Heat Transfer 112, 21, 1990b, Inst. Heat Mass Transfer 33(5), 877) has suggested that the temperature field around a propagating crack tip might exhibit some of the characteristics of hyperbolic heat conduction. In this paper a corrected solution of the hyperbolic heat conduction equation for a travelling point source is derived. Then an experimental estimate of the active plastic zone (heat generating zone) at a crack tip is used for various experimental conditions to examine the possible effects of hyperbolic heat conduction around a propagating crack tip. Finally, using the actual experimental conditions of Zehnder and Rosakis (1991) Zehnder and Kallivayalil (1991) and Mason and Rosakis (1992) it is shown that no effects of hyperbolic heat conduction are observed around a propagating crack tip. It is seen that, due to adiabatic conditions at the crack tip during these experiments, the solution of the hyperbolic heat equation is indistinguishable from the solution of the parabolic heat conduction equation for crack propagation in steel.     

Properties of eigenfunction expansion form and relative integral for a crack with completely closed surfaces

The important property of the eigenfunction expansion form found by Chen [Engng Fracture Mech. 22, 673–686 (1985)] is found as the pseudo-orthogonal property. The analysis of this property and relative integral for a semi-infinite crack with completely closed surfaces in homogeneous plane elasticity is studied in detail. It is found that the integral proposed by Bueckner [in Mechanics of Fracture, Vol. 1, pp. 239–314 (1973)] and Chen is no longer path-independent in this circumstance. The differences between the present investigation and that of Chen are discussed.     

Interaction of a crack with certain microcrack arrays

Interaction of a crack with microcracks (modelling “damage”) can significantly alter the stress concentration at the crack tip. Certain important effects of interaction—shielding effect (“toughening by microcracking”), amplification effect, influence of the orientations of microcracking and irregularities in its patterns, change of the character of interaction (shielding to amplification and vice versa) with change of the mode of loading, etc.—are demonstrated on several microcrack systems. It appears that these relatively simple systems exhibit the essential features of the crack-damage interactions. Consideration is based on the method of analysis of elastic solids with many cracks proposed recently [Kachanov, Int. J. Fracture 28, R11–R19 (1985); Kachanov, Int. J. Solids Structures (in press)] and briefly presented here.     

Dynamic plastic response of circular plates in a damping medium

The motion of a simply supported circular plate of rigid-plastic material is studied. The motion is produced by a uniformly distributed impulsive velocity [Jones and de Oliveira, ASME J. appl. Mech. 47, 27–34 (1980)]. The material of the plate is assumed to obey the Tresca yield criterion with the inclusion of shear yield. The effect of damping by the surrounding medium on the plate motion is examined.     

Plane-stress crack-tip fields for pressure-sensitive dilatant materials

In this paper we present plane-stress crack-tip stress and strain fields for pressure-sensitive dilatant materials. A hydrostatic stress-dependent yield criterion and the normality flow rule are used to account for pressure-sensitive yielding and plastic dilatancy. The material hardening response is specified by a power-law relation. The plane-stress mode I singular fields are found in a separable form similar to the HRR fields (Hutchinson, J. Mech. Phys. Solids 16, 13–31 and 337–347, 1968; Rice and Rosengren, J. Mech. Phys. Solids 16, 1–12, 1968). The angular variations of the fields depend on the material hardening exponent and the pressure sensitivity parameter. Our low-hardening solutions for different degrees of pressure sensitivity agree well with the corresponding perfectly plastic solutions. An important aspect of the effects of pressure-sensitive yielding and plastic dilatancy on crack-tip fields is the lowering of the opening stress and the hydrostatic stress directly ahead of the crack tip. This effect, similar to that under plane-strain conditions (Li and Pan, to appear in J. Appl. Mech. 1989), has implications in the material toughening observed in some ceramic and polymeric composites.     

An examination of long-rod penetration

The one-dimensional modified Bernoulli theory of Tate [J. Mech. Phys. Solids 15, 287–399 (1967)] is often used to examine long-rod penetration into semi-infinite targets. The theory is summarized and the origins of the target resistance term examined. Numerical simulations were performed of a tungsten-alloy, long-rod projectile into a semi-infinite hardened steel target at three impact velocities sufficiently high to result in projectile erosion. The constitutive responses of the target and projectile were varied parametrically to assess the effects of strain hardening, strain-rate hardening, and thermal softening on penetration response. The results of one of the numerical simulations were selected to compare and contrast in detail with the predictions of the Tate model.     

Thermal and mechanical load induced damage behaviour of a low alloy steel: Mechanisms and modelling

A series of experiments, including macroscopic damage measurement and in situ microscopic observation at room temperature and tensile tests at eight different temperatures ranging from 20 to 900°C, is carried out. Mechanical load induced ductile damage evolution law and micromechanisms are presented, where damage evolution law is measured through a new a.c. potential system and the micromechanisms of damage and fracture are observed through an in situ technique in conjunction with a scanning electron microscope (SEM) equipped with a tensile platform. A continuum damage mechanics (CDM) model for ductile fracture proposed by Wang [Engng Fracture Mech. 42, 177–183 (1992)] is employed to model and to analyse the evolution law of damage in the steel. Comparison of experimental and modelling results is presented and good agreement is found. The effect of stress triaxiality on damage evolution is also discussed in the framework of CDM. The effect of temperature rise on tensile properties including Young's modulus, yield and ultimate tensile strength and ductility (elongation and reduction in area), is also reported.     

A method to determine the fracture toughness of unidirectional fibre reinforced composites in mode II (forward shear), using a thin tubular specimen

A method has been developed, using thin tubular specimens, to determine the fracture toughness of unidirectional fibre reinforced composites in Mode II. The tubular specimens were loaded under torsion and hence produced pure shear at the crack tips located on the circumference of the tube. The cracks were made parallel to the transverse axis and in the mid-length of the tube. Calibration factors for Mode II were obtained. The stress-intensity factors at instability, K_IIR(INS) were obtained by experiments on thin tubular specimens through a compliance matching procedure. The crack growth resistance at instability and the corresponding initial strain energy release rates were independent of the initial crack in the range of crack length investigated. The stress-intensity factor obtained by the thin torsion tube method is slightly higher than the stress-intensity factor at instability, K_IIR(INS) obtained by the method developed by Giare for end cracked beams [Engng. Fracture Mech. 20, 11–21 (1984)]. This method may be applied to a different geometrical shapes and hence may be useful in determining the fracture toughness of any closed geometrical sections.     

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.     

An energy based mode III fracture criterion for composites

In this work, a new fracture hypothesis referred to as the Z-criterion is developed for mode III cracks in orthotropic composite materials. The new theory predicts critical crack propagation conditions and the crack propagation direction. The Z-criterion (Zhang et al., Engng Fracture Mech. 34, 749–769 (1989) (S-criterion) (Sih, Proc. 10th SES Annual Meeting, 221–234, Boston (1975)) removes certain deficiencies by considering separately the dilatational and distortional strain energy density factors. It suggests that under mode I conditions, crack initiation is controlled by the dilatational strain energy density factor and for mode II and mode III conditions, crack initiation is controlled by the distortional strain energy density factor (Zhang et al. A new Z-criterion… submitted to Engng Fracture Mech.). These controlling parameters allow extension to mixed mode and three dimension crack analysis. Eleven different composite materials are used to test and verify the proposed Z-criterion.     

Crack initiation condition in the specimens of ductile materials

In this paper, the elasto-plastic Finite Element Method was used to simulate the ductile fracture initiation of four kinds of specimens made of low-carbon steel No. 20 (Chinese steel), and the damage parameter V_D was calculated for these specimens. The results showed that the damage mechanics criterion V_D proposed by the author and B. X. Yang [Engng Fracture Mech. 27, 371–386 (1987)], could be applied to predict the crack initiation. Also, the relationship between the damage parameter V_Dc and the crack tip opening displacement was discussed in this study.     

A study on estimation of damage accumulation of glass fibre reinforce plastic (GFRP) composites under a block loading situation

Many cumulative damage theories have been used in lifetime calculation of GFRP composite components. However, it is well known that linear damage accumulation models are inadequate for predicting the cumulative damage in GFRP compositeas due to their dominant viscoelastic characteristics. This paper discusses the outcomes of application of damage accumulation models proposed by Palmgren-Miner [Miner MA. Cumulative damage in Fatigue. J Appl Mech 1945;12(September):A159–64], Broutman and Sahu [Broutman LJ, Sahu SA. New theory to predict cumulative fatigue damage. In: Fiberglass reinforced plastics, composite materials: testing and design (second conference), ASTM STP 497; 1972. p. 170–88], Hashin and Rotem [Hashin Z, Rotem A. A cumulative damage theory of fatigue failure. J Mater Sci Eng 1978;(34):147–60] and Epaarachchi and Clausen [Epaarachchi Jayantha A, Clausen Philip D. On predicting the cumulative fatigue damage in glass fibre reinforced plastic (GFRP) composites under step/discrete loading. Composites Part A: Appl Sci Manuf 2005;36(9):1236–45], to calculate the lifetime of GFRP composite samples under repeated block loading situations.     

Analysis of in-plane transonically propagating interface crack with a finite contact zone

The report of Lambros and Rosakis [(1995) J Mech Phys Solids 43(2): 169–188] has focused attention on steady-state transonic interfacial crack growth accounting for the phenomenon of crack face contact in elastic/rigid bimaterial but could not handle issues relating to energy transmission across the interface. The present paper attempts to provide a complete explicit expression of the asymptotic fields induced by transonically propagating interfacial crack in elastic/elastic bimaterial for in-plane case. The energy distribution on the contact area, crack tip and two singular characteristic lines is analysed thoroughly and compared with the dynamic separated J-integrals. The length of the contact zone is also discussed briefly by establishing energy fracture criterion that satisfies contact condition. The two-dimensional in-plane asymptotic deformation field surrounding the contact area of a crack propagating transonically along an elastic/elastic bimaterial interface is observed and discussed thoroughly.     

A computational approach to determining the depth of surface flaws by the ACPD technique

The boundary element method is used to analyze the ACPD (alternating current potential drop) field perturbed by a semi-elliptical surface flaw in a metallic sheet. The depth of the penetration of the alternating current is assumed to be small as compared to the crack depth. This allows us to adopt the “unfolding” technique developed by Dover et al. [ASTM STP 722, 401–427 (1981)], which reduces the problem to a two-dimensional surface Laplacian field. This surface potential field is determined for different surface cracks with crack aspect ratios ranging from 0.2 to 2. To facilitate the use of these results, an empirical formula is developed based on the numerical results. A simple inverse analysis methodology is also developed for determining the crack depth for semi-elliptical surface flaws of known surface length with measured potential drop readings.     

Development of double hinge mechanisms in a bent cantilever subjected to an out-of-plane force pulse

In a previous paper [Y. L. , T. X. and S. R. , Double hinge modes in the dynamic response of plastic cantilever beams subjected to step loading. Int. J. Impact Engng 7, 401–413 (1988)] double hinge mechanisms were shown to satisfy all the necessary equations for the initial deformation mechanism of a range of bent cantilevers subjected to an out-of-plane tip force. The present study examines the transient behaviour of such mechanisms when the cantilever is subjected to a force pulse of finite duration. The change in the mechanism as the hinges travel and the partitioning of the dissipation of the input energy are described and compared with the behaviour of a straight cantilever subjected to a force pulse at its tip.     

Fracture of fibrous metal matrix composites—III. effect of imperfection geometry and heat treatment

The work of Dvorak et al. and Bahei-El-Din et al. (1989) on fracture of unidirectionally reinforced boron/aluminum specimens with a center notch is extended here for specimens with various imperfection geometries and heat treatment. The experimental results indicate that long, discrete plastic shear zones similar to those found at the notch tips are present in all specimens. The measured fracture strength was not affected by the notch shape, but was affected by the heat treatment. Finite element analysis of selected specimens indicated that the fracture criterion proposed in parts I and II is applicable to as-fabricated or annealed B/A1 specimens with any notch geometry. Namely, failure is controlled by a critical ratio of the largest principal stress to off-axis unnotched strength in the principal direction, in a small representative volume in the vicinity of the notch. This criterion, however, does not apply for specimens tested in the overaged (T6) condition.