Ted L. Anderson

A framework to correlate a/W ratio effects on elastic-plastic fracture toughness (J c )

Single edge-notched bend (SENB) specimens containing shallow cracks (a/W < 0.2) are commonly employed for fracture testing of ferritic materials in the lower-transition region where extensive plasticity (but no significant ductile crack growth) precedes unstable fracture. Critical J-values Jc) for shallow crack specimens are significantly larger (factor of 2–3) than the Jc)-values for corresponding deep crack specimens at identical temperatures. The increase of fracture toughness arises from the loss of constraint that occurs when the gross plastic zones of bending impinge on the otherwise autonomous crack-tip plastic zones. Consequently, SENB specimens with small and large a/W ratios loaded to the same J-value have markedly different crack-tip stresses under large-scale plasticity. Detailed, plane-strain finite-element analyses and a local stress-based criterion for cleavage fracture are combined to establish specimen size requirements (deformation limits) for testing in the transition region which assure a single parameter characterization of the crack-tip stress field. Moreover, these analyses provide a framework to correlate Jc)-values with a/W ratio once the deformation limits are exceeded. The correlation procedure is shown to remove the geometry dependence of fracture toughness values for an A36 steel in the transition region across a/W ratios and to reduce the scatter of toughness values for nominally identical specimens.

Continuum and micromechanics treatment of constraint in fracture

Two complementary methodologies are described to quantify the effects of crack-tip stress triaxiality (constraint) on the macroscopic measures of elastic-plastic fracture toughness J and Crack-Tip Opening Displacement (CTOD). In the continuum mechanics methodology, two parameters J and Q suffice to characterize the full range of near-tip environments at the onset of fracture. J sets the size scale of the zone of high stresses and large deformations while Q scales the near-tip stress level relative to a high triaxiality reference stress state. The materials fracture resistance is characterized by a toughness locus Jc(Q) which defines the sequence of J-Q values at fracture determined by experiment from high constraint conditions (Q∼0) to low constraint conditions (Q<0). A micromechanics methodology is described which predicts the toughness locus using crack-tip stress fields and critical J-values from a few fracture toughness tests. A robust micromechanics model for cleavage fracture has evolved from the observations of a strong, spatial self-similarity of crack-tip principal stresses under increased loading and across different fracture specimens. We explore the fundamental concepts of the J-Q description of crack-tip fields, the fracture toughness locus and micromechanics approaches to predict the variability of macroscopic fracture toughness with constraint under elastic-plastic conditions. Computational results are presented for a surface cracked plate containing a 6:1 semielliptical, a=t/4 flaw subjected to remote uniaxial and biaxial tension. Crack-tip stress fields consistent with the J-Q theory are demonstrated to exist at each location along the crack front. The micromechanics model employs the J-Q description of crack-front stresses to interpret fracture toughness values measured on laboratory specimens for fracture assessment of the surface cracked plate.

On the application of R-curves and maximum load toughness to structures

An approximate procedure is presented which allows a ductile fracture analysis to be performed with a single fracture toughness value measured at maximum load in a small-scale test. This maximum load toughness value is used to predict an R-curve which is then used to predict maximum stress and crack extension. Predictions from this approach are compared with experimental data from 20 wide-plate specimens made from various ductile materials. A limited number of these specimens are also analyzed using experimental R-curves in order to investigate the effect of the assumed shape of the R-curve on predictions. In addition, an analysis is presented which allows one to determine the critical tearing modulus required for a structure to exhibit collapse controlled failure. Potential applications of these analyses are discussed.

Application of fractal geometry to damage development and brittle fracture in materials

Abstract This article represents a first attempt to apply the concepts of fractal geometry to damage development in materials. Two extremes of material behavior were considered. In the case of unstable brittle propagation of microcracks, application of fractal geometry and weakest link statistics lead to the well-known Weibull distribution for fracture stress. The Weibull slope (shape parameter) is equal to twice the fractal dimension of the flaw distribution. For the case of stable microcrack growth, a number of simplifying assumptions led to a closed-form expression for the change in effective modulus with an increment of damage. Although an oversimplification, this latter analysis illustrates the potential value of fractal geometry in modeling damage development. Future work will be directed towards developing these initial results further.

Numerical procedures to model ductile crack extension

Abstract Experimental studies demonstrate a significant increase in the cleavage fracture toughness ( J c ) for shallow notched bend and tensile specimens. Dodds and Anderson have proposed a micromechanics model for cleavage that predicts the specimen size dependence of fracture toughness. This effort extends the micromechanics model to include the influence of ductile crack extension prior to cleavage. The present discussion focuses on the numerical techniques required to include finite-strain plasticity and crack growth. Key results are presented for the small-scale yielding problem to demonstrate the usefulness of these numerical procedures to model ductile crack growth.

Ductile and brittle fracture analysis of surface flaws using CTOD

A reference stress method is used to analyze both brittle and ductile fracture in structures containing surface flaws. Crack-tip opening displacement (CTOD) is used as the fracture-toughness input, althoughJ-based reference stress analyses are also possible. Both detailed and simplified analyses for brittle and ductile fracture are described. A brittle fracture analysis which takes account of stress concentrations, secondary stresses and stress gradients is presented, together with a complete ductile tearing analysis which utilizes a single CTOD value measured at maximum load. In addition, two simplified approaches are proposed: a yield-before-break criterion for brittle fracture and a critical learing modulus for ductile fracture.

Assessing the Dominant Mechanism for Size Effects on CTOD Values in the Ductile-to-Brittle Transition Region

There has been some uncertainty in the field of fracture mechanics as to whether shifts in the ductile-to-brittle transition with specimen size are caused by statistical sampling effects or constraint effects. Fracture toughness data for three carbon-manganese steels were analyzed to examine the effectiveness of each model in predicting the results of different sized specimens. The data set used in this investigation contains nearly 500 crack tip opening displacement (CTOD) values for various geometries of single edge notched bend (SENB) specimens with thicknesses ranging from 10 to 100 mm. A limited amount of data for single edged notched (SENT) specimens and side grooved SENB specimens was also included. It was found that the mechanism which accounts for size effects most effectively depends on the amount of plastic flow prior to fracture. Under conditions of small scale yielding, high constraint is maintained in both small and large specimens. In this region the Landes and Shaffer statistical sampling model appears to work well for explaining the higher average toughness of small specimens. However, when the ligament yields prior to fracture, the shifts in transition observed with specimen size cannot be explained by statistical sampling effects alone. The temperature at which net section yielding first occurs tends to shift upward as (1) the specimen thickness increases, (2) the ligament length is decreased (in a bend specimen), or (3) the mode of loading is changed from tension to bending. When the ligament yields, the plastic deformation relaxes the crack tip constraint and the brittle-to-ductile transition becomes steep. The relaxation of crack tip constraint occurs more rapidly and at lower temperatures in smaller specimens. This gives rise to a steeper transition curve and a shift in transition temperature which cannot be accounted for by statistical effects. Thus as the critical CTOD increases the relative contribution of statistical sampling on size effects decreases and constraint effects tend to dominate.