On modelling cracks in orthotropic plates under biaxial loading: synthesis and summary

Abstract

A B S T R A C T The model of a crack with a process zone is considered and generalized to orthotropic materials. It is assumed that a material in the process zone satisfies a strength condition of arbitrary form. Based on the crack model, the fracture of an orthotropic cracked plate under biaxial loading is studied. The crack is directed along one of the anisotropy axes with external loads being applied in parallel and perpendicularly to it. The influence of the biaxiality of external loading on the critical state of the cracked plate is analysed within the framework of the critical crack opening displacement and critical J-integral criteria. Numerical solution is obtained using the Mises-Hill and Gol'denblat-Kopnov strength criteria. Theoretical results are compared with experimental data obtained by testing specimens made of structural metals.Keywords biaxial loading; crack model; fracture; orthotropic plate; process zone. N O M E N C L A T U R E a ij= elastic constants d = process zone length E i = elastic moduli along the orhotropy axes F = function of a strength criterion G 12 = shear modulus J = J-integral J c = critical value of J-integral K I = stress intensity factor for the mode I crack l = half-crack length L = length of half-crack with a process zone p * , q * = ultimate loads p (0) * = ultimate load in uniaxial tension p (m) * = ultimate load for macrocrack S i = roots of a characteristic equation T 0 = function of elastic constants v = displacement of a cracked body β i = imaginary part of roots of a characteristic equation β = β 1 /β 2 δ = crack opening displacement δ c = critical value of crack opening displacement ν 12 = Poisson's ratio σ 0x , σ 0y = ultimate strengths in the x and y axis directions, respectively σ s 0x , σ s 0y = ultimate strengths in tension along the x-and y-axis σ p 0x , σ p 0y = ultimate strengths in compression along the x-and y-axis Correspondence: A. A. Kaminsky.

Mode I Crack Initiation in Orthotropic Viscoelastic Plates Under Biaxial Loading

“…where µ i , γ i , i = 1,…, 7 are given by (14). In this case, in view of (10), for the safe loading, we obtain…”

“…where δ 0 (x, t) and T * are determined from the corresponding elastic solution as follows: [14] δ 0 (…”

“…To investigate long-term crack propagation by means of the theory of subcritical crack growth in orthotropic viscoelastic materials [1], we use the modified Dugdale's model [14]. The following assumptions are made:…”

“…An approach based on the concept of crack-tip process zone and on the additional necessity to satisfy the strength criterion in this zone was proposed in [14]. This approach makes it possible to generalize the Dugdale model of cracks to the case of orthotropic materials.…”

“…In the present work, the subcritical crack growth in an orthotropic viscoelastic plate under biaxial loading is investigated on the basis of the proposed crack model [14]. The durations of the incubation and transition periods of subcritical crack growth are determined on the basis of the Volterra principle and the solution of the corresponding problem of elasticity.…”