Some approximate treatments of fracture statistics for polyaxial tension

Abstract

A frequently used approximate treatment of fracture statistics for polyaxial stress states assumes that the probability of survival is the product of the probabilities of survival of the structure for the principal stresses applied individually. The present paper shows that this assumption is generally unconservative and therefore the approximation serves as a lower bound to the failure probability. A simple technique is given for finding an upper bound in cases of biaxial tension prox~ded the uniaxial fracture behavior is described satisfactorily by Weibull's two-parameter formula. The upper bound is a good approximation when in high stress regions the stresses are equibiaxial, or nearly so, as in laterally loaded or spinning disks.

Structural integrity assessment of glass components in Concentrated Solar Power (CSP) systems

“…(19) needs to be calculated. The influence of the fracture criteria on the failure prediction under multiaxial stresses was discussed in [12,22].…”

“…For some standardized specimen configurations and loading modes, analytical solutions were given in [20][21][22][23] and shown in the following examples:…”

“…and(24) into Eq (22),. the time to failure t f can be calculated as: one design strength diagram may be generated from the above procedures.The time to failure t f versus equivalent stress as a function of probability of failure is shown inFig.…”

Mechanical Properties of Dense Cordierite Discs Sintered by Solar Radiation Heating

“…By using the Weibull statistics, however, the concerned differences can be accounted for and prediction of the data to be acquired under equibiaxial stress condition from the data acquired under multiaxial stress state or vice versa might become feasible. Batdorf 21) and Breder et al 22) reviewed this problem for the fixture geometry used in the present study and drew the following relationship for the effective area A eff(ROR) (mm 2 ) for the ring-on-ring type equibiaxially tested specimen:…”

An assessment of the state of the art in predicting the failure of ceramics: Final report

“…Petrovic (1976D, 1976E) compared the maximum normal stress, coplanar SERR, and noncoplanar SERR criteria for combined Mode I and Mode II opening. Batdorf (1977) compared the maximum normal stress and coplanar SERR criteria. Later, Batdorf (1978A) compared the maximum normal stress, noncoplanar SERR, and SED criteria for uniaxial and equibiaxial tension.…”