Bernard Budiansky

Elastic moduli of a cracked solid

Abstract Calculations on the basis of the self-consistent method are made for the elastic moduli of bodies containing randomly distributed flat cracks, with or without fluid in their interiors. General concepts are outlined for arbitrary cracks and explicit derivations together with numerical results are given for elliptic cracks. Parameters are identified which adapt the elliptic-crack results to arbitrary convex crack shapes. Finally, some geometrical relations involving randomly distributed cracks and their traces on cross-sections are presented.

On the elastic moduli of some heterogeneous materials

Abstract A heuristic analysis is given for the determination of the elastic moduli of a composite material, the several constituents of which are each isotropic and elastic. The results are intended to apply to heterogeneous materials composed of contiguous, more-or-less spherical grains of each of the phases.

Matrix fracture in fiber-reinforced ceramics

Abstract A fiber-reinforced ceramic subject to tensile stress in the fiber direction can undergo extensive matrix cracking normal to the fibers, while the fibers remain intact. In this paper, the critical conditions for the onset of widespread matrix cracking are studied analytically on the basis of fracture mechanics theory. Two distinct situations concerning the fiber-matrix interface are contemplated : (i) unbonded fibers initially held in the matrix by thermal or other strain mismatches, but susceptible to frictional slip, and (ii) fibers that initially are weakly bonded to the matrix, but may be debonded by the stresses near the tip of an advancing matrix crack. The results generalize those of the Aveston-Cooper-Kelly theory for case (i). Optimal thermal strain mismatches for maximum cracking strength are studied, and theoretical results are compared with experimental data for a SiC fiber, lithium-alumina-silicate glass matrix composite.

Compressive failure of fibre composites

Abstract A review of experimental data and elementary theoretical formulas for compressive failure of polymer matrix fibre composites indicates that the dominant failure mode is by plastic kinking. Initial local fibre misalignment plays a central role in the plastic kinking process. Theoretical analyses and numerical results for compressive kinking are presented, encompassing effects of strain-hardening, kink inclination, and applied shear stress. The assumption of rigid fibres is assessed critically, and the legitimacy of its use for polymer matrix composites is established.

Theory of Buckling and Post-Buckling Behavior of Elastic Structures

Publisher Summary The general theory of buckling and post-buckling behavior of elastic structures has led to a considerable amount of research in this field. A comprehensive survey provides a very useful bibliography, together with an overview of the achievements, status, and goals of post-buckling theory. The chapter provides a unified, general presentation of the basic theory in a form suitable for application to a wide variety of special problems. This will be done with the help of the succinct notation of functional analysis, which turns out to be remarkably appropriate for the purpose. Simple conceptual models can illustrate with remarkable verisimilitude many of the essential characteristics of the buckling and post-buckling behavior of more complicated structural systems. Before undertaking a general analysis of arbitrary elastic structures, such models are exploited in order to expose basic concepts of bifurcation buckling, snap buckling, imperfection-sensitivity, load-shortening relations, and stability.

Small-Scale Crack Bridging and the Fracture Toughness of Particulate-Reinforced Ceramics,

Abstract T heoretical analyses of small-scale bridging of crack surfaces by elastic-ideally plastic springs are presented and applied to the study of the fracture toughness of ceramics reinforced by small particles. The dependence of toughening on particle size, concentration, strength, and ductility is explored, and relations between toughening and bridge length at fracture are given. Available experimental information is examined in the light of the analyses.

Void Growth and Collapse in Viscous Solids

Summary Deformation of an isolated void in an infinite block of linearly or nonlinearly viscous material is studied for remote axisymmetric stressing. The material is isotropic and incompressible with a power-law dependence of strain-rate on stress. Included in the family of materials are a linearly viscous solid and a rigid–perfectly plastic solid at the extreme limit of nonlinearity. Evolution of the void shape and size is analyzed in detail for voids starting as spheres in the linearly viscous material under all possible combinations of remote axisymmetric stressing. Asymptotic, or self-similar, shapes towards which the voids evolve are exhibited as are the associated rates of growth or collapse. Under conditions of high remote triaxial stressing the growth-rate of the asymptotic void is found to be identical to that of a spherical void with the same volume. The influence of nonlinearity on the growth-rate and deformation of a spherical void is investigated. Under high triaxiality conditions the behavior of a void in the nonlinearly viscous or rigid–perfectly plastic material is qualitatively different from that of a void in a linearly viscous material. In particular, a void in a nonlinear block undergoing tensile straining with sufficiently large superimposed remote hydrostatic tension grows more rapidly in directions perpendicular to the straining direction than along it and becomes significantly oblate. Asymptotic growth-rates are estimated numerically for the nonlinear materials. The results for the isolated void are used in a simple, approximate way to investigate the roles of material nonlinearity and stressing conditions on the strain required for ductile failure by void growth and coalescence.

DYNAMIC BUCKLING OF IMPERFECTION-SENSITIVE STRUCTURES.

Small geometrical imperfections in some structures can be responsible for large reductions in their static buckling strengths. As is well known, a thin shell is often very imperfection-sensitive in this sense, with a perfect specimen sometimes having a “classical” buckling strength several times higher than that of an imperfect one. Many analytical studies have sought to correlate reductions in buckling strength with assumed initial imperfections of various sizes and shapes. Such studies may eventually provide the quantitative information needed for the establishment of a statistical theory of buckling, which would relate the probability of buckling under a given static load to the spectrum of imperfections (see [1]). But at the present time, the design of shells leans heavily on experiment, and analysis has been mainly useful in identifying imperfection-sensitive structures and in establishing, in a qualitative way, the degree of this sensitivity.

Dynamic buckling estimates.

Dynamic buckling of imperfection sensitive models, specifically cylindrical shells under axial compression

Toughening by aligned, frictionally constrained fibers

Abstract T he M ode I fracture toughness of a brittle material reinforced by aligned brittle fibers is studied theoretically. The fibers are assumed to slip relative to the matrix when a critical interface shear stress is reached, and the toughening action of the fibers is presumed to be due to bridging of crack faces in the vicinity of the crack front. The toughening due to the fiber reinforcement is related to basic parameters associated with the related problem of steady-state matrix cracking in the presence of intact fibers. Bridge lengths at fracture and fracture resistance curves are calculated.