The discussion on the application of theory of failure is in the context of assessment of the

Margin of Safety, MoS, (FoS -1) under static load up to Design Limit Load, DLL, up to which

the structural behaviour is generally linearly elastic. In the context of aircraft structures

designed to meet the applicable FAR 23 or FAR 25 compliance requirements, no permanent

(plastic) deformations are allowed up to DLL; and the aircraft structure should withstand the

Design Ultimate Load, DUL, for at least 3 Seconds before any structural collapse; implied in

the latter statement is that the aircraft structure can, in fact, fail under DUL after 3 seconds of 

sustaining the DUL, and still the structure would deemed to have complied with the DUL

requirement under FAR 25. One may recall, and as widely published, the Airbus-380 wing

failure occurred much before the DUL. The compliance with the DUL test under FAR 25 has

to be demonstrated through an ult imate load test only ; any computational compliance is

only to establish the confidence of the design/test group before the DUL test is actually

carried out; the computational results will not be accepted by the regulatory authorities as

proof of compliance of FAR 25 requirement (it was, however, accepted under FAR 23, and

has been dispensed with under FAR 25). For ducti le metal l ic structures the von Mises 

fai lure cri ter ion is u sed to demonstrate the required MoS at DLL against the design 

al lowable where the structu ral behaviour is elast ic. 

The structural behaviour beyond DLL and up to DUL depends up on the structural design

and the material stress-strain response of the material: it could be linearly elastic, non-

linearly elastic or even plastic (if the von Mises stress reaches the yield strength of the

material before DUL is reached) or a combination of all of these. The stress engineer would

continue the analysis of the structure beyond DLL by application of the appropriate analysis

procedures by deploying the appropriate structural and material behaviour models for 

different sections of the load-stress response curve.

The analysis of the structure under plastic behaviour is governed by the theory of plasticity,

ToP, and is coded into many industry-standard FE codes. One needs, however, to have a

sound knowledge of the ToP and the material stress-strain behaviour and its mathematical

representation to deploy these analysis codes successfully for understanding the elasto-

plastic behaviour of the structure, and to endorse the structural safety up to DUL and stand

by it till the successful DUL test. Normally, regions of high stress gradients like boundaries of 

cut-outs, re-entry corners, thickness discontinuities and bolt holes etc. need such a detailed

elasto-plastic analysis. It may be noted that the material should have significant plastic strain

at ultimate load (typical of a ductile material like 2023 Al-Cu alloy which has up to 5% plastic

strain at DUL) to allow significant plastic strain at DUL to keep the maximum stress level

below the material ultimate stress. The yield criterion to deploy, the flow rule etc. are matters

of detail and material ‘stress strain behaviour ’ dependent. Of cour se, von Mis es yield 

cri ter ion is appr opriate and de-facto fo r elasto-plast ic respon se of du cti le materials 

beyond th e yield. 

The structural behaviour under fatigue loads (with or without cracks), DTA etc. are different

and most important topics beyond the scope of the present topic under discussion.

S. Sridhara Murthy