Calibration of Weibull stress parameters using fracture toughness data

AbstractThe Weibull stress model for cleavage fracture of ferritic steels requires calibration of two micromechanics parameters $$(m,\sigma _u ) $$ . Notched tensile bars, often used for such calibrations at lower-shelf temperatures, do not fracture in the transition region without extensive plasticity and prior ductile tearing. However, deep-notch bend and compact tension specimens tested in the transition region can provide toughness values under essentially small-scale yielding (SSY) conditions to support Weibull stress calibrations. We show analytically, and demonstrate numerically, that a nonuniqueness arises in the calibrated values, i.e., many pairs of $$(m,\sigma _u ) $$ provide equally good correlation of critical Weibull stress values with the distribution of measured (SSY) fracture toughness values. This work proposes a new calibration scheme to find $$(m,\sigma _u ) $$ which uses toughness values measured under both low and high constraint conditions at the crack front. The new procedure reveals a strong sensitivity to m and provides the necessary micromechanical values to conduct defect assessments of flawed structural components operating at or near the calibration temperature in the transition region. Results of a parameter study illustrate the expected values of m for a typical range of material flow properties and toughness levels. A specific calibration is carried out for a mild structural steel (ASTM A36).

[1]  Robert H. Dodds,et al.  Specimen Size Requirements for Fracture Toughness Testing in the Transition Region , 1991 .

[2]  R. H. Dodds,et al.  Loading rate effects on cleavage fracture of pre-cracked CVN specimens: 3-D studies , 1997 .

[3]  Kim Wallin,et al.  Constraint effects on reference temperature, T0, for ferritic steels in the transition region , 1998 .

[4]  G. T. Hahn,et al.  The Influence of Microstructure on Brittle Fracture Toughness , 1984 .

[5]  Stanley T. Rolfe,et al.  Effects of crack depth on elastic-plastic fracture toughness , 1991 .

[6]  B. Moran,et al.  A general treatment of crack tip contour integrals , 1987 .

[7]  Claudio Ruggieri,et al.  A transferability model for brittle fracture including constraint and ductile tearing effects: a probabilistic approach , 1996 .

[8]  Albert H. Moore,et al.  POINT AND INTERVAL ESTIMATORS, BASED ON M ORDER STATISTICS, FOR THE SCALE PARAMETER OF A WEIBULL POPULATION WITH KNOWN SHAPE PARAMETER , 1965 .

[9]  K Wallin,et al.  Statistical Aspects of Constraint with Emphasis on Testing and Analysis of Laboratory Specimens in the Transition Region , 1993 .

[10]  K. W. Schuler,et al.  Shock pulse attenuation in a nonlinear viscoelastic solid , 1973 .

[11]  J. Rice,et al.  Limitations to the small scale yielding approximation for crack tip plasticity , 1974 .

[12]  Robert H. Dodds,et al.  Numerical investigation of 3-D constraint effects on brittle fracture in SE(B) and C(T) specimens , 1996 .

[13]  A. Pineau,et al.  A local criterion for cleavage fracture of a nuclear pressure vessel steel , 1983 .

[14]  D. Munz,et al.  Estimation procedure for the Weibull parameters used in the local approach , 1992, International Journal of Fracture.

[15]  Kim Wallin,et al.  The scatter in KIC-results , 1984 .

[16]  D Stienstra,et al.  A Theoretical Framework for Addressing Fracture in the Ductile-Brittle Transition Region , 1994 .

[17]  M. Toyoda,et al.  A statistical approach for fracture of brittle materials based on the chain-of-bundles model , 1995 .

[18]  F. Marino,et al.  Electrical resistivity and structural relaxation in Fe75TM5B20 amorphous alloys (TM = Ti, V, Cr, Mn, Co, Ni) , 1984 .

[19]  D. Munz,et al.  THE SIZE EFFECT OF MICROSTRUCTURAL IMPLICATIONS OF THE WEAKEST LINK MODEL , 1990 .

[20]  Anthony G. Evans,et al.  A statistical model of brittle fracture by transgranular cleavage , 1986 .

[21]  J. Gurland,et al.  A statistical model for low temperature cleavage fracture in mild steels , 1989 .

[22]  Claudio Ruggieri,et al.  Numerical evaluation of probabilistic fracture parameters using WSTRESS , 1998 .

[23]  A. J. Carlsson,et al.  Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials , 1973 .

[24]  Andrew H. Sherry,et al.  Local Approach to Fracture Applied to Reactor Pressure Vessel : Synthesis of a Cooperative Programme Between EDF, CEA, Framatome and AEA , 1996 .

[25]  F. Mudry,et al.  A local approach to cleavage fracture , 1987 .

[26]  M. R. Goldthorpe,et al.  The Effect of Temperature and Specimen Geometry on the Parameters of the "Local Approach" to Cleavage Fracture , 1996 .

[27]  C. J. McMahon,et al.  Initiation of cleavage in polycrystalline iron , 1965 .

[28]  T. Hughes.  Generalization of selective integration procedures to anisotropic and nonlinear media , 1980 .

[29]  Robert H. Dodds,et al.  A framework to correlate a/W ratio effects on elastic-plastic fracture toughness (Jc) , 1991 .

[30]  M. Williams,et al.  On the Stress Distribution at the Base of a Stationary Crack , 1956 .

[31]  Kim Wallin,et al.  Statistical model for carbide induced brittle fracture in steel , 1984 .

[32]  Arne S. Gullerud,et al.  WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture , 1998 .

[33]  C. Shih,et al.  Ductile crack growth−III. Transition to cleavage fracture incorporating statistics , 1996 .