by Berezovski, Arkadi; Maugin, Gerard A.

A non-equilibrium description of the crack propagation in the framework of the material setting is applied to the straight-through crack in brittle materials. The velocity of the crack is determined in terms of the driving force by means of non-equilibrium jump relations at the crack front. Theoretical results are compared with experimental data for Homalite-100.

DOI: 10.1007/s10704-007-9053-x
Online Date: 2/23/2007
Print publication date: 1/1/2007
View article on SpringerLink

by Mier, Jan G. M.

Fracture processes in brittle disordered materials like many geo-materials (rock, ice, concrete, cement, etc.) are a trade off between local stress concentrations caused by the heterogeneity of such materials, and local strength. At those locations where the ratio between stress and strength exceeds a critical threshold value, cracking may initiate. Depending on the size of the cracks they can be arrested by stronger and stiffer elements in the structure of the material, or they will propagate and become critical. Critical cracks lead to localisation of deformations and to softening. In currently popular cohesive crack models still some continuum ideas remain, namely the notion of stress, whereas the localisation of deformations is handeled correctly by means of displacements. During softening the macro-crack traverses the specimen’s cross-section, thereby gradually decreasing the effective load-carrying area. This growth process is affected both by structure (specimen) size and boundary conditions, and a better description of softening may be achieved by using load and displacement as state variables. In this paper, a new method of modelling fracture is proposed by using fracture potentials (F − r relations) at various observation scales, from atomistic and molecular to macroscopic. The virtual material can be interpreted as being built up from spherical elements; the fracture potential describes the interactions between the spheres. Since the spherical elements interact at their contacts-points only, a force-separation law (F–r) suffices. Size/scale effects are dealt with directly in the F–r relation; size/scale effects on strength are merely a special point in the entire description and do not require a separate law.

DOI: 10.1007/s10704-007-9050-0
Online Date: 2/21/2007
Print publication date: 1/1/2007
View article on SpringerLink

by

DOI: 10.1007/s10704-007-9052-y
Online Date: 2/20/2007
Print publication date: 1/1/2007
View article on SpringerLink

by Daphalapurkar, Nitin P.; Lu, Hongbing; Coker, Demir; Komanduri, Ranga

Dynamic crack growth is simulated by implementing a cohesive zone model in the generalized interpolation material point (GIMP) method. Multiple velocity fields are used in GIMP to enable handling of discrete discontinuity on either side of the interface. Multilevel refinement is adopted in the region around the crack-tip to resolve higher strain gradients. Numerical simulations of crack growth in a homogeneous elastic solid under mode-II plane strain conditions are conducted with the crack propagating along a weak interface. A parametric study is conducted with respect to varying impact speeds ranging from 5 m/s to 60 m/s and cohesive strengths from 4 to 35 MPa. Numerical results are compared qualitatively with the dynamic fracture experiments of Rosakis et al. [(1999) Science 284:1337–1340]. The simulations are capable of handling crack growth with crack-tip velocities in both sub-Rayleigh and intersonic regimes. Crack initiation and propagation are the natural outcome of the simulations incorporating the cohesive zone model. For various impact speeds, the sustained crack-tip velocity falls either in the sub-Rayleigh regime or in the region between $$\sqrt 2 c_{S}$$ (c

_S
is the shear wave speed) and c

_D
(c

_D
is the dilatational wave speed) of the bulk material. The Burridge–Andrews mechanism for transition of the crack-tip velocity from sub-Rayleigh to intersonic speed of the bulk material is observed for impact speeds ranging from 9.5 to 60 m/s (for normal and shear cohesive strengths of 24 MPa). Within the intersonic regime, sustained crack-tip velocities between 1.66 c

_S
(or 0.82 c

_D
) and 1.94 c

_S
(or 0.95 c

_D
) were obtained. For the cases simulated in this work, within the stable intersonic regime, the lowest intersonic crack-tip velocity obtained was 1.66 c

_S
(or 0.82 c

_D
).

DOI: 10.1007/s10704-007-9051-z
Online Date: 2/14/2007
Print publication date: 1/1/2007
View article on SpringerLink

by Christensen, Richard; Miyano, Yasushi

The lifetime prediction methodology developed here is an addendum to and a generalization of that given earlier by Christensen and Miyano [Christensen RM, Miyano Y (2006) Int J Frac 137:77–87]. The previous results were not sufficiently general to model some of the results in the intermediate time ranges. The present results still retain the kinetic crack formalism but include more general forms that are in accordance with data. This new method admits both deterministic and probabilistic forms. Specific applications are given for creep rupture and constant strain rate programs. Possible applications are for any materials types whose very long term creep rupture behavior takes a power law form.

DOI: 10.1007/s10704-006-9049-y
Online Date: 2/14/2007
Print publication date: 1/1/2007
View article on SpringerLink

by Ellyin, Fernand; Ozah, Folarin

Three-dimensional finite element method is utilized to analyze the plasticity-induced crack closure (PICC) phenomenon in a cracked plate under variable amplitude loading conditions: the effect of a single spike tensile overload, and also the case of a single compressive overload (underload). To accurately capture the PICC process the choice of material model employed is of significant importance, therefore this paper considers a relatively new model, the Ellyin-Xia model, and the more widely employed kinematic hardening model. The study shows significant difference in the results obtained while employing the two models.

DOI: 10.1007/s10704-006-9048-z
Online Date: 2/14/2007
Print publication date: 1/1/2007
View article on SpringerLink