Ductile tearing and discrete void effects on cleavage fracture under small-scale yielding conditions

Abstract Over the mid-to-upper region of the ductile-to-brittle transition region, transgranular cleavage and ductile tearing define two competing failure mechanisms in ferritic steel. At metallurgical scales (≲50 μm), formation and growth of the voids driving ductile crack extension likely alter the local stress fields acting on the smaller inclusions that trigger cleavage fracture. Here we study the effects of void growth on cleavage fracture by modeling discrete cylindrical voids lying on the crack plane ahead of the crack tip within a small-scale yielding (SSY) boundary layer model. These discrete voids have a spacing, D, within a highly refined crack-front region. This enables identification of both single void growth and multiple void growth mechanisms that depend primarily on the initial void porosity, f0. The crack grows in this model by release of nodal reactions (enforcing zero displacement) along the ligament (symmetry plane) between the blunted crack tip and closest void when the void obtains a specified critical porosity. This process grows the crack in discrete increments of size equal to the length of an intervoid ligament. Continued external loading leads to subsequent void growth and crack extensions through additional node releases. The external loads at the point of each crack extension define the crack growth resistance (JR) curves. This enables comparison with conventional JR–Δa curves obtained using computational cell (Gurson–Tvergaard) analyses. The Weibull stress model is then employed to quantify the stress concentration effects on the probability of cleavage fracture. We describe a non-dimensional function, h ( J ^ ) , to represent stress concentration effects on the Weibull stress in a convenient framework ( J ^ = J / D σ 0 denotes a non-dimensional loading for SSY analyses). These h-functions also reflect the increase in volume of material sampled as the crack grows from the original tip to the first void, the second void, etc. The h-functions vary with material flow properties, initial porosity (f0), critical porosity (fc), Weibull modulus (m), and T-stress (Tσ) or constraint level.

[1]  M. F. Kanninen,et al.  Inelastic Behavior of Solids , 1970, Science.

[2]  J. Knott,et al.  The relationship between fracture toughness and microstructure in the cleavage fracture of mild steel , 1976 .

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

[4]  Robert H. Dodds,et al.  Constraint effects on the ductile-to-brittle transition temperature of ferritic steels: a Weibull stress model , 2000 .

[5]  Claudio Ruggieri,et al.  Numerical modeling of ductile crack growth in 3-D using computational cell elements , 1996 .

[6]  G. A. Webster,et al.  Weibull Stress Solutions for 2-D Cracks in elastic and Elastic-Plastic Materials , 1998 .

[7]  Jd Landes,et al.  Statistical Characterization of Fracture in the Transition Region , 1980 .

[8]  J. Rice.  A path-independent integral and the approximate analysis of strain , 1968 .

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

[10]  Robert H. Dodds,et al.  Calibration of the Weibull stress scale parameter, σu, using the Master Curve , 2004 .

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

[12]  R. H. Dodds,et al.  Probabilistic Modeling of Brittle Fracture Including 3-D Effects on Constraint Loss and Ductile Tearing , 1996 .

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

[14]  L. Cheng,et al.  Transition from ductile tearing to cleavage fracture: A cell-model approach , 1997 .

[15]  J. Hutchinson,et al.  The relation between crack growth resistance and fracture process parameters in elastic-plastic solids , 1992 .

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

[17]  V. Tvergaard.  Material Failure by Void Growth to Coalescence , 1989 .

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

[19]  C. Ruggieri,et al.  Micromechanics characterization of constraint and ductile tearing effects in small scale yielding fracture , 2001 .

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

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

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

[23]  Viggo Tvergaard,et al.  Two mechanisms of ductile fracture: void by void growth versus multiple void interaction , 2002 .

[24]  K. B. Broberg,et al.  The cell model of materials , 1997 .

[25]  Deutsche Gesellschaft für Zerstörungsfreie Prüfung,et al.  Defect assessment in components : fundamentals and applications , 1991 .

[26]  I. C. Howard,et al.  MESH INDEPENDENT CELL MODELS FOR CONTINUUM DAMAGE THEORY , 1994 .

[27]  A. Gurson.  Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media , 1977 .

[28]  N. Aravas,et al.  FINITE ELEMENT ANALYSIS OF VOID GROWTH NEAR A BLUNTING CRACK TIP , 1985 .

[29]  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 .

[30]  Robert M. McMeeking,et al.  Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture , 1977 .

[31]  Viggo Tvergaard,et al.  Effects of nonlocal damage in porous plastic solids , 1995 .

[32]  Claudio Ruggieri,et al.  Influence of threshold parameters on cleavage fracture predictions using the Weibull stress model , 2001 .

[33]  Jonas Faleskog,et al.  Micromechanics of coalescence—I. Synergistic effects of elasticity, plastic yielding and multi-size-scale voids , 1997 .

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

[35]  Z. H. Li,et al.  Finite element analysis of non‐local effects in ductile fracture , 2000 .

[36]  R. H. Dodds,et al.  Simulation of ductile crack growth using computational cells: numerical aspects , 2000 .

[37]  Fong Shih,et al.  Analysis of ductile to cleavage transition in part‐through cracks using a cell model incorporating statistics , 1999 .

[38]  Robert H. Dodds,et al.  Coupling of the Weibull stress model and macroscale models to predict cleavage fracture , 2004 .

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