The T-criterion applied to ductile fracture

Theocaris, P. S.; Andrianopoulos, N. P.

doi:10.1007/bf01130617

Cited by 132 publications

(54 citation statements)

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“…In this paper a theoretical investigation of crack branching was based on the study of the elastodynamic stress field developed in [8]. This stress field was applied separately to the T-criterion [11][12][13] and to the S2-criterion [14,15].…”

Section: Introductionmentioning

confidence: 99%

The variation of the dynamic modulus on crack propagation modes

Papadopoulos

Theocaris

1987

Int J Fract

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The variation of the elastic modulus due to the dynamic propagation of a crack and its influence on the instability of this dynamic process was studied, based on the theory of the T-criterion of failure of the material. Conditions for an eventual bifurcation of the moving crack were established according to this criterion. Furthermore, a comparison was undertaken between the results derived from the T-criterion and an improving modification of the S-criterion, called S 2-criterion, which Was based on the two-term expressions of the elastic stress field around the crack. While in the T-criterion the dilatational strain energy density, T~, was calculated on the respective Mises elastic plastic boundary where the distortional component of strain energy density was constant, in the S2-criterion the core region was defined by the respective initial curve of the dynamic caustic.It was shown that the changes of the dynamic modulus and Poisson's ratio, depending on the relative crack velocity, were the main factors creating these instability-and bifurcation-phenomena of the moving cracks. Nomograms of the critical relative velocities of bifurcation versus the dynamic modulus and Poisson's ratio were plotted and compared satisfactorily with experimental data. It was indicated that, while the T-criterion gave satisfactory results all over the range of velocities and moduli, the S 2-criterion gave comparable results only for brittle or semi-brittle cases. List of symbolsrl, 01, r:, 02, r, 0 = kl, ~ = E,, E, = Y, V i Cl~ C 2 t) = = zs,~ = dW/dV = ro = TD = (7 0 O=_ ~b = crack tip stresses referred to Cartesian coordinate system. polar coordinate system centered at crack tip. stress intensity factors. elastic moduli of the material. Poisson's ratios of the material. velocities of the longitudinal and the shear waves, respectively. crack velocity. the mass density of the material. parametric equations of caustics. elastic strain-energy density. dilatational strain-energy density. distortional strain-energy density. yield stress of the material. angle of birfucation.

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Section: Introductionmentioning

confidence: 99%

The variation of the dynamic modulus on crack propagation modes

Papadopoulos

Theocaris

1987

Int J Fract

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“…The three most used [35] are the criteria of maximum tangential (circumferential) stress [36], maximum energy release rate [37] and minimum strain energy density [38]. Other criteria include the criterion of maximum dilatational strain energy density [39] and the criterion of minimum accumulated strain energy [11]. There is no general agreement about which criterion should be used for a given material, but Bittencourt, et al [24] have shown that the three former criteria predict basically the same crack growth trajectory for poly(methyl methacrylate) (PMMA), which is a brittle material.…”

Section: Evaluation Of the Direction For Further Crack Growthmentioning

confidence: 99%

A review of fatigue crack propagation modelling techniques using FEM and XFEM

Rege

Lemu

2017

IOP Conf. Ser.: Mater. Sci. Eng.

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The study of the dissipation heat flow and the acoustic emission during the fatigue crack propagation in the metal A N Vshivkov, A Yu Iziumova, I A Panteleev et al. noAbstract. Fatigue is one of the main causes of failures in mechanical and structural systems. Offshore installations, in particular, are susceptible to fatigue failure due to their exposure to the combination of wind loads, wave loads and currents. In order to assess the safety of the components of these installations, the expected lifetime of the component needs to be estimated. The fatigue life is the sum of the number of loading cycles required for a fatigue crack to initiate, and the number of cycles required for the crack to propagate before sudden fracture occurs. Since analytical determination of the fatigue crack propagation life in real geometries is rarely viable, crack propagation problems are normally solved using some computational method. In this review the use of the finite element method (FEM) and the extended finite element method (XFEM) to model fatigue crack propagation is discussed. The basic techniques are presented, together with some of the recent developments. IntroductionComponents which are subjected to fluctuating loads are found virtually everywhere: Vehicles and other machinery contain rotating axles and gears, pressure vessels and piping may be subjected to pressure fluctuations (e.g. water hammer) or repeated temperature changes, structural members in bridges are subjected to traffic loads and wind loads, while those in ships and offshore structures are subjected to the combination of wind loads, wave loads and currents. If the components are subjected to a fluctuating load of a certain magnitude for a sufficient amount of time, small cracks will nucleate in the material. Over time, the cracks will propagate, up to the point where the remaining cross-section of the component is not able to carry the load, at which the component will be subjected to sudden fracture [1]. This process is called fatigue, and is one of the main causes of failures in structural and mechanical components [2]. In order to assess the safety of the component, engineers need to estimate its expected lifetime. The fatigue life is the sum of the number of loading cycles required for a fatigue crack to nucleate/initiate, and the number of cycles required for the crack to propagate until its critical size has been reached [2,3]. In this paper, computational methods to estimate the lifespan of a propagating crack whose initial geometry is known will be considered.Estimations of the fatigue crack propagation rate, da/dN, are normally based on a relation with the range of the stress intensity factor, ΔK, which is a linear elastic fracture mechanics (LEFM) parameter for quantifying the load and geometry of the crack. Paris, Gomez and Anderson [4] first proposed the existence of such a relation in 1961, and its simplest form is the Paris law [5]:

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“…T Several others criteria have been proposed, for instance the zero shear stress criterion by Maiti et al [11], the M-criterion proposed by Kong et al [12] based on the maximum value of the stress triaxiality ratio /  is an equivalent stress which can be assumed to be equal to the Von Mises stress), the maximum dilatational strain energy density criterion (T-criterion) proposed by Theocaris et al [13][14][15]. From experimental tests, it has been observed that the crack propagation direction usually tends to follow the local or global minimum extension of the plastic core region.…”

Section: Mixed-mode Crack Propagation Criteriamentioning

confidence: 99%

Crack path dependence on inhomogeneities of material microstructure

Brighenti¹,

Carpinteri²,

Spagnoli³

et al. 2012

Frattura Ed Integrità Strutturale

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ABSTRACT.Crack trajectories under different loading conditions and material microstructural features play an important role when the conditions of crack initiation and crack growth under fatigue loading have to be evaluated. Unavoidable inhomogeneities in the material microstructure tend to affect the crack propagation pattern, especially in the short crack regime. Several crack extension criteria have been proposed in the past decades to describe crack paths under mixed mode loading conditions. In the present paper, both the Sih criterion (maximum principal stress criterion) and the R-criterion (minimum extension of the core plastic zone) are adopted in order to predict the crack path at the microscopic scale level by taking into account microstress fluctuations due to material inhomogeneities. Even in the simple case of an elastic behaviour under uniaxial remote stress, microstress field is multiaxial and highly non-uniform. It is herein shown a strong dependence of the crack path on the material microstructure in the short crack regime, while the microstructure of the material does not influence the crack trajectory for relatively long cracks.SOMMARIO. L'andamento dei percorsi di frattura sotto diverse condizioni di carico e caratteristiche microstrutturali del materiale ha un ruolo importante nella determinazione delle condizioni di nucleazione e propagazione a fatica della fessura. Inevitabili disomogeneità nella microstruttura del materiale tendono a influenzare il percorso di propagazione della fessura, particolarmente nel caso di fessure corte. In letteratura sono stati proposti numerosi criteri volti a descrivere i percorsi di frattura in condizioni di modo misto. Nel presente lavoro, sia il criterio di Sih (della massima tensione principale) che il criterio R (della minima estensione della zona plastica) sono stati adottati per predire i percorsi di frattura alla scala microscopica tenendo conto di fluttuazioni delle microtensioni dovute alle disomogeneità del materiale. Anche nel semplice caso di comportamento elastico del materiale in presenza di tensione monoassiale remota, il campo tensionale alla microscala risulta essere multiassiale e non uniforme. Viene evidenziata una significativa dipendenza del percorso di frattura nel caso di fessure corte dalla microstruttura del materiale, mentre nel caso di fessure lunghe tale dipendenza risulta trascurabile.

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The T-criterion applied to ductile fracture

Cited by 132 publications

References 2 publications

The variation of the dynamic modulus on crack propagation modes

The variation of the dynamic modulus on crack propagation modes

A review of fatigue crack propagation modelling techniques using FEM and XFEM

Crack path dependence on inhomogeneities of material microstructure

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