design considerations for aluminum hull structures - Ship Structure ...

-49-be more critical if elonga%fon were to be considered as a limiting factor.Referring to the typical stress-strain curve in Figure 12 below~ two areasaxe considered: The area under the curve in the elastic r~ge~ and the area-betweenthe yield and ultimate strengths, designated Al and A2 resPective~Y:UltimateTensileStrength ~ Rupture-7FIG. 12 Stress-Strain Relationshipsfor AluminumStressElongationThe areas AI and AP are both important in studying the overall responseof a material to loading, even though Al is far smaller than AP. These areasrepresent the quantity stress times elongation, which is proportional toforce times distsmce, or work. Axes Al therefore represents the work requiredto exceed the elastic limit of the material, and falls within the area inwhich structures are normally loaded. Within this area, at any given stresslevel, aluminum has a 3 to 1 advantage over steel because of its lower modulusof elasticity.The area A2 represents the work associated with the plastic strain energyof_,t&he material, between the elastic range and rupture. Tn this area, due toitsgreater eio~atio~ steel has an approximate 2 to 1 advantage over aluminum.If it is assumed that the importance ofareas A1 amd A2 is identical, whichis implicit in the Equation 1, it is apparent that aluminum’s advantage in theelastic zone more than offsets its lower total elongation. Thus, differencesin material elongation do not directly affect Equation 1.Long-Term Loading - Long-term loading implies consideration of the anticipatedstress levels which the hull will experience throughout its life, inconjunction with the low cycle fatigue strength of the hull material. For thisspecific study, the following proce~ure has ~een adopted:(a)(b)(c)(d)(e)Estimate the life cycle histogram, bending moment versus numberof cycles, for the steel bulk carrier, and convert th~s to equivalentbending st~ess, based on the steel hull girder section modulusas built.Develop a fatigue (S-N) curve for hull steel, ASTM A131-61.Determine the ratio of fatigue strength to hullstress throughout the life of the vessel. Thissidered a safety factor on fatigue failure.girder bendingcan be con-Apply these same ratios to the S-N curve of the selected aluminumalloy, thus establishing a curve of allowable life cycle bendingstress for the aluminum hull girder.Determine the area (A) under the two life-cycle bending stresscurves. The required hull girder section modulus to satisfyfati~ue requirements is then as follows: