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An unified gate-level fault model for interconnect opens and bridges is proposed. Defects are modeled as constrained multiple line stuck-at faults. A novel feature of the proposed fault model is its flexibility to accommodate increasing levels of accuracy. Additionally the model does not require accurate device level circuit models to achieve desired accuracy. Efficient methods for fault simulation and test generation are discussed and experimental results on benchmark circuits and industrial designs are presented. The experimental results presented show that the tests generated using simpler versions of the proposed fault model achieve higher defect coverage than the tests using two currently popular methods to derive high defect coverage tests. PreliminariesIn this section we give a brief description of the MLSF fault model used for interconnect opens proposed in [5]. An open with infinite resistance will cause some lines to float. The gates driven by the fanout branches of floating lines may interpret the logic state of the floating line differently. This is referred to as Byzantine effect in this work. The Byzantine effect at a floating line with k branches was modeled in [5] by 2(2 k -1) MLSFs on the k fanout branches. (2 k -1) of these faults are for the case when the floating line is driven to zero and the remaining (2 k -1) faults are for the case when the floating is driven * The research of S. M.

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A B S T R A C T This paper presents a method for evaluating constraint effects on probabilistic elasticplastic analysis of cracks in ductile solids. It is based on fracture parameters J and Q, correlation between Q and J-resistance curve of the material, and J-tearing theory for predicting fracture initiation and instability in cracked structures. Based on experimental data from small-scale fracture specimens, correlation equations were developed for fracture toughness at crack initiation and the slope of the J-resistance curve as a function of constraint condition. The random parameters may involve crack geometry, tensile and fracture toughness properties of the material, and applied loads. Standard reliability methods were applied to predict probabilistic fracture response and reliability of cracked structures. The results suggest that crack-tip constraints have little effect on the probability of crack initiation. However, the probability of fracture instability can be significantly reduced when constraint effects are taken into account. Hence, for a structure where some amount of stable crack-growth can be tolerated, crack-tip constraints should be considered for probabilistic fracture-mechanics analysis.Keywords crack; crack-tip constraint; elastic-plastic fracture mechanics; probabilistic fracture mechanics; J-integral; Q parameter; J-resistance curve; J-Q analysis; singleedged-notched bend specimens. N O M E N C L A T U R Ea=crack size; crack depth of single-edged-notched bend specimen B=thickness of single-edged-notched bend specimen C(Q)=constraint-based slope of J-resistance curve C (Q)=normalized slope of J-resistance curve D ij , E ij , F ij , G ij , H ij =constant coefficients D, E, F, G, H=matrices involving coefficients, D ij , E ij , F ij , G ij , H ij E=Young's modulus f X (x)=joint probability density function of X h 1 =dimensionless plastic influence function J=J-integral J e =elastic component of J J p =plastic component of J J R (Da)=J-resistance curve J R (Da, Q)=constraint-dependent J-resistance curve J Ic (Q)=constraint-based mode-I plane-strain fracture toughness at initiation J Ic (Q)=normalized mode-I plane-strain fracture toughness at initiation J(X )=J-integral as a function of random vector, X k init =probability ratio for fracture initiation k ins =probability ratio for fracture instability K I =mode-I stress-intensity factor n=Ramberg-Osgood exponent n j =jth component of unit outward normal to integration path, dC N=number of input random variables P=load; load on single-edged-notched bend specimen I N T R O D U C T I O Nconstraint effects on fracture-mechanics evaluation of cracked structures. Current elastic-plastic fracture-mechanics analysis of cracks typically involves fracture toughness properties of It is now well known in the fracture-mechanics community that a single fracture parameter, e.g. the materials measured using high-constraint specimen geometries, e.g. deeply cracked three-point bend specimens.J-integral, alone may not be adequate to describe cracktip condition...

This paper presents a probabilistic methodology for fracture-mechanics analysis of off-center cracks in pipes subject to pure bending moment. It is based on: (1) a new analytical approximation of the J-integral; (2) statistical models of uncertainties in loads, material properties, and crack geometry; and (3) standard computational methods of structural reliability theory. The proposed analytical equations were applied to a probabilistic fracture-mechanics analysis of off-center cracks in pipes. The second-order reliability method was used to determine the probabilistic characteristics of the J-integral and failure probability based on the initiation of crack growth. Numerical examples are presented to illustrate the proposed methodology. The results show that the failure probability strongly depends on the offcenter crack angle and is generally lower than that of a pipe with a symmetrically centered crack. Hence, simplifying an off-center crack by a symmetrically centered crack can produce significant conservatism in predicting failure probabilities. In addition, uncertainty in the offcenter crack angle, if it exists, can increase the failure probability of pipes. ᭧