How coupon and element tests reduce conservativeness in element failure prediction

• The effect of the number of coupon and element tests on structural weight was studied.
• A combination of the sampling uncertainty in measuring material variability and the uncertainty in the failure prediction was modeled.
• Element tests are important for a typical case of larger uncertainty in the failure prediction.
• The convolution integral was used to model the combination of the uncertainties.

Structural elements, such as stiffened panels, are designed by combining material strength data obtained from coupon tests with a failure theory for 3D stress field. Material variability is captured by dozens of coupon tests, but there remains epistemic uncertainty due to error in the failure theory, which can be reduced by element tests. Conservativeness to compensate for the uncertainty in failure prediction (as in the A- or B-basis allowables) results in a weight penalty. A key question, addressed here, is what weight penalty is associated with this conservativeness and how much it can be reduced by using coupon and element tests. In this paper, a probabilistic approach is used to estimate the conservative element failure strength by quantifying uncertainty in the element strength prediction. A convolution integral is used to efficiently combine uncertainty from coupon tests and that from the failure theory. Bayesian inference is then employed to reduce the epistemic uncertainty using element test results. The methodology is examined with typical values of material variability (7%), element test variability (3%), and the error in the failure theory (5%). It is found that the weight penalty associated with no element test is significant (20% heavier than an infinite number of element tests), and it is greatly reduced by more element tests (4.5% for 5 element tests), but the effect of the number of coupon tests is much smaller.