Method and article of manufacture for estimating material failure due to crack formation and growth

A method for identifying a cracking plane in an elastic material under the action of a tensile multiaxial strain history, the method comprising the steps of:

• calculating a cracking energy density Wc for a material plane, said cracking energy density being incrementally defined by,
• dWc={overscore (σ)}·d{overscore (ε)}
• with
• {overscore (σ)}=σ{overscore (r)}={overscore (r)}Tσ, d{overscore (ε)}=dε{overscore (r)}
• where dWc is the incremental cracking energy density, σ is the stress tensor, d{overscore (ε)} is the strain differential and {overscore (r)} is a unit vector normal to the material plane;
• repeating the step of calculating the cracking energy density Wc for a selected set of material planes;
• and
• identifying the cracking plane based on the cracking energy density calculations.

An article of manufacture comprising a program storage medium readable by a computer and embodying one or more instructions executable by the computer to perform a method for estimating a fatigue life in a material that undergoes a strain history, the method comprising:

• defining a plurality of spatial planes that collectively represent the material planes;
• calculating cracking energy densities corresponding to the plurality of spatial planes wherein the cracking energy density of a spatial plane indicates the energy available to propagate a crack in that spatial plane;
• and
• estimating the fatigue life based on the calculated cracking energy densities.