A Re-Examination of Failure Analysis and Root Cause Determination

13the stress conditions are known for a given material, then it is possible to calculate thesize of crack that can be tolerated in that material without having the crack grow further.The following equation shows those conditions. A crack will propagate if:σ≥βKIcπ awhere σ (sigma) is the fracture stress, β (beta) is a dimensionless shape factor and a isthe crack length for a crack with only one tip (i.e., not an internal crack, but one openingat a surface). Handbooks for engineering calculations have tables of values for Beta fordifferent geometries.If the fracture toughness of the material is known, the fracture stress or critical cracksize of a component can be calculated if the stress intensity factor is known.This calculation will allow• the determination of “permissible flaw size,”• the calculation of the stress necessary to cause catastrophic failure• the determination of the load on a component at the time of failure• the determination as to whether adequate materials were used in manufacturing• the determination as to whether a part design was adequate.If the system that failed is well documented, then operational stresses can becalculated. For example, it can be determined how great the load was on a certain partwhen it failed. The load history may also be known throughout the time that the part wasused. These data can be used to calculate the toughness, given a knowledge of thecrack size at the time of final failure. This will show whether the part performedaccording to the specifications for it.On the other hand, if the stresses are not known, then toughness still can be estimatedfrom materials handbooks, again knowing the crack size and the area of the remainingsound metal at the time of failure.If neither toughness nor stresses are known, toughness can be estimated from physicaltesting, using Charpy-impact tests on pieces of the material. The stresses at failure canbe determined by back-calculation and it can then be said if the part failed fromoverload.Much can be also done to quantify conditions from fatigue failures. The rate of crackgrowthcan be estimated from a knowledge of the number of striations per unit length ofcrack perpendicular to the crack front. If the stresses are known, the stress intensity canbe inferred, and the adequacy of the material for the use conditions can be determined.From a knowledge of the known stresses, the crack size at fracture and the crackgrowth-rate, estimates may be made as to whether or not the material had beenmisused.