Simulation of spallation in brittle solids

A new model of dynamic fracture for brittle materials based on Perzyna's[1] idea and Seaman's experimental results[2] is developed. Numerical simulations of metal uranium[3] spalling process in its impact tests are carried out with the model. Fair agreement between the computation and experimental data has been obtained.     

Porosity dependence of strength in brittle solids

The effect of pore size and pore volume fraction on strength in brittle solids is evaluated. The analysis considers that the strength degradaton of a solid containing a large number of spherical pores is due to a strong effect of porosity on Young's modulus. Each pore is assumed to possess radial or annular flaws emanating from the pore surface whose lengths are considered to be independent of pore size. The effect of stress concentration induced by the presence of the pore is included in the equation for strength through the Young's modulus dependence of porosity originally developed using the concept of crack opening displacement. It is shown that the strength of a solid containing spherical pores is controlled by the pore size, pore volume fracton and the radial (or annular) crack size to pore size ratio. Predicted variation of strength with pore volume fraction is tested against experimental data for glass and polycrystalline alumina.     

Micro-cracks informed damage models for brittle solids

A class of micro-cracks informed damage models for describing the softening behavior of brittle solids is proposed, in which damage evolution is treated as a consequence of micro-crack propagation. The homogenized stress–strain relation in the cracked microscopic cell defines the degradation tensor, which can be obtained by the equivalence between the averaged strain energy of the microscopic cell and the strain energy density of the homogenized material. This energy equivalence relationship serves as an energy bridging vehicle between the damaged continuum and the cracked microstructure. Several damage evolution equations are obtained by this energy bridging method. The size effect of the micro-cracks informed damage law is characterized through the microscopic cell analysis, and the proper scaling of the characterized damage evolution functions to eliminate mesh dependency in the continuum solution is introduced.     

The brittle fracture of metals

A study has been made of the theory of the brittle fracture of metals, where plastic deformation arises during the cleavage process. By the use of X-rays, the magnitude of this plastic work has been investigated on single crystal and polycrystal cleavage surfaces. A theoretical study has also been made of the depth of the plastic zone in single crystals with varying crack velocity.     

A new damage model for microcrack-weakened brittle solids

In the present paper, a micromechanically based damage model for microcrack-weakened solids is developed. The concept of the domain of microcrack growth (DMG) is defined and used to describe the damage state and the anisotropic properties of brittle materials. After choosing an appropriate fracture criterion of microcrack, we obtain the analytical expression of DMG under a monotonically increasing proportional plane stress. Under a complex loading path, the evolution equation of DMG and the overall effective compliance tensor of damaged materials are given. The project supported by National Natural Science Foundation of China     

On possible causes of brittle fracture

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 137–141, May–June, 1988.     

A nonlocal theory for brittle fracture

In this paper, a nonlocal theory of fracture for brittle materials has been systematically developed, which is composed of the nonlocal elastic stress fields of Griffith cracks of mode-I, II and III, the asymptotic forms of the stress fields at the neighborhood of the crack tips, and the maximum tensile stress criterion for brittle fracture. As an application of the theory, the fracture criteria of cracks of mode-I, II, III and mixed mode I–II, I–III are given in detail and compared with some experimental data and the theoretical results of minimum strain energy density factor.     

Kinematic features of the brittle fracture phenomenon

Summary Normal-fracture surfaces of various high-polymers were investigated with the aid of light microscopy. The common fracture pattern is discussed in relation with the kinematic fracture picture introduced bySmekal (1–3). Attention is paid to radial traces and hyperbolic traces, as well as to other morphological features. With the aid of the morphological picture and results of mechanical surface roughness measurements, the three-dimensional density (volume population) of fracture sources could, at polymethylmethacrylate, be roughly estimated. The geometry of fracture sources of polymethylmethacrylate was elucidated by means of electron microscopy. Supplementary experiments performated at normal-fracture surfaces of polymethylmethacrylate showed the effect of a 90°-rotation of the largest principal stress upon the critical condition of inhomogeneities.

---

Zusammenfassung Bruchflächen verschiedener Hochpolymeren wurden lichtmikroskopisch untersucht. Die Bruchfiguren werden an Hand des kinematischen Bildes des Bruchvorgangs, wie esSmekal entwickelte, betrachtet. Besondere Aufmerksamkeit wurde den radialen und hyperbolischen Spuren sowie den anderen morphologischen Zügen gewidmet. Mit Hilfe des morphologischen Bildes und der Ergebnisse von mechanischen Messungen der Oberflächenrauhigkeit konnte grob für Polymethylmethacrylat die 3-dimensionale Dichte (Volumenhäufigkeit) der Quellen für den Bruch abgeschätzt werden. Die geometrische Form der Bruchquellen für Polymethylmethacrylat wurde elektronenmikroskopisch geklärt. Ergänzende Experimente an Normal-Bruchflächen von Polymethylmethacrylat zeigen den Effekt einer 90°-Drehung der größten Hauptspannung auf die kritische Inhomogenitätsbedingung.

---

---

Presented at the conference Flow, Fatigue and Failure held in Leeds on January 8th and 9th, 1959, by the British Society of Rheology.     

Phase-field models for brittle and cohesive fracture

In this paper we first recapitulate some basic notions of brittle and cohesive fracture models, as well as the phase-field approximation to fracture. Next, a critical assessment is made of the sensitivity of the phase-field approach to brittle fracture, in particular the degradation function, and the use of monolithic versus partitioned solution schemes. The last part of the paper makes extensions to a recently developed phase-field model for cohesive fracture, in particular for propagating cracks. Using some simple examples the current state of the cohesive phase-field model is shown.     

A theory for brittle fracture in compression

A symmetric cylindrical body composed of brittle material, if compressed along its generators may collapse progressively, firstly through catastrophic loss of material adjacent to its lateral surface(s). With increase of the compressive load the reduced cylinder, unable to resist, sunders. The first stage of this type of failure can be explained by the assumed existence of latent interior cracks which open abruptly on a curved, symmetric interior surface when the total energy of the body reaches a critical value determined by the geometry of the initial fracture surface.     

The role of shear stresses in brittle fracture

Using the three-dimensional model for brittle fracture developed earlier by S.A.F. Murrell and P.J. Digby (1970,1972) shear stress concentrations are calculated for brittle bodies and the relative roles of tensile and shear stresses in the fracture process are considered. It is found that the maximum shear stress and the maximum tensile stress occur at different places on a crack, and that there is a wide range of stress states for which they do not occur on the same crack. Furthermore, if the theoretical cleavage strength is σ_max and the theoretical shear strength is τ_max, then cleavage precedes inelastic shear and brittle fracture is possible, for suitable stress systems, when $\text{σ}{}_{\max }\text{<}\text{2τ}{}_{\mathrm{<mtext>max</mtext>}}\text{(1 ? ν)}$, where ν is the Poisson's ratio of the solid matrix. This appears to be in accordance with empirical observations.     

Scattered fracture of porous materials with brittle skeleton

A model of damage accumulation in a porous medium with a brittle skeleton saturated with a compressible fluid is formulated in the isothermal approximation. The model takes account of the skeleton elastic energy transformation into the surface energy of microcracks. In the case of arbitrary deformations of an anisotropic material, constitutive equations are obtained in a general form that is necessary and sufficient for the objectivity and thermodynamic consistency principles to be satisfied. We also formulate the kinetics equation ensuring that the scattered fracture dissipation is nonnegative for any loading history. For small deviations from the initial state, we propose an elastic potential which permits describing the principal characteristics of the behavior of a saturated porous medium with a brittle skeleton. We study the acoustic properties of the material under study and find their relationship with the strength criterion depending on the accumulated damage and the material current deformation. We consider the problem of scattered fracture of a saturated porous material in a neighborhood of a spherical cavity. We show that the cavity failure occurs if the Hadamard condition is violated.     

Effect of microstructure on fracture of brittle materials: Unified approach

A theoretical approach to the fracture of brittle solids based on crack opening displacement and energy rate criterion is presented. The approach allows for the prediction of elastic (Young’s modulus) and fracture (fracture strength and thermal shock) response of a brittle material containing spherical pores and polycrystalline solids containing anisotropic residual stresses.     

Continuum interpolation of stress fields in brittle fracture

The locally nonlinear behavior of crack stresses is first represented by adjustable boundary conditions near the crack tip. The actual boundary conditions are then determined by continuity conditions imposed on a general parameterized solution. The thus modified formulation yields finite crack tip stresses consistent with atomistic and other hybrid models of brittle fracture.     

Stable growth of fracture in brittle aggregate materials

Fracture of concrete is analyzed by combining the resistance curve (R-curve) approach with linearly elastic solutions for the energy release rate resulting from the quasi-static crack model of Wnuk, analogous to the D-BCS model of a stationary crack used in describing quasi-brittle fracture in metals. The R-curve, representing the crack length dependence of the energy consumed per unit fracture extension, is calculated using the concept of the energy separation rate associated with a finite crack growth steps. To simplify calculations, the tensile stress transmitted across the nonlinear zone ahead of the fracture front is assumed to be uniformly distributed over the entire nonlinear zone, even though in reality it must be a gradually declining stress resulting in strain-softening; and an infinite elastic medium loaded at infinity is assumed. These assumptions permit an easy solution with the help of Green's function for an infinite elastic medium. Application to bodies of finite size then requires assuming the nonlinear zone (fracture process zone) to be negligible with regard to specimen dimensions, crack length and ligament length. Even though this assumption is not always realistic, the end results, which are of practical importance, appear reasonable. The analysis leads to a nonlinear first-order ordinary differential equation for the R-curve, which is integrated numerically. The R-curves calculated in this manner can be closely fitted to data from previous fracture tests. Only two parameters, characterizing the initial and the final lengths of the nonlinear zone, need to be adjusted to test data.     

Uniqueness and minimum theorems for a multifield model of brittle solids

Some minimum theorems potentially useful to construct numerical schemes related to quasi-static evolution of damage in brittle elastic solids are proposed. The approach is that of multifield theories, with a second-order damage tensor describing the microcrack density. The use of damage entropy flux and damage pseudo-potential are both investigated.