Presentation on theme: "Failure criteria for laminated composites"— Presentation transcript:
1Failure criteria for laminated composites Defining “failure” is a matter of purpose.Failure may be defined as the first event that damages the structure or the point of structural collapse.For composite laminates we distinguish between “first ply failure” when the first ply is damaged and “ultimate failure” when the laminate fails to carry the load.Ultimate failure requires “progressive failure” analysis where we reduce the stiffness of failed plies and redistribute the load.
2Failure criteria for isotropic layers Failure is yielding for ductile materials and fracture for brittle materials.Every direction has same properties so we prefer to define the failure based on principal stresses. Why?We will deal only with the plane stress condition, which will simplify the failure criteria. Then principal stresses areWhat about the third principal stress?
3Maximum normal stress criterion For ductile materials strength is same in tension and compression so criterion for safety isHowever, criterion is rarely suitable for ductile materials.For brittle materials the ultimate limits are different in tension and compression
4Maximum strain criterion Similar to maximum normal stress criterion but applied to strain.Applicable to brittle materials so tension and compression are different.What is wrong with the figure?
5Maximum shear stress (Tresca) criterion Henri Tresca ( ) French MEMaterial yields when maximum shear stress reaches the value attained in tensile test.Maximum shear stress is one half of the difference between the maximum and minimum principal stress.In simple tensile test it is one half of the applied stress. So criterion is
6Distortional Energy (von Mises) criterion Richard Edler von Mises (1883 Lviv, 1953 Boston).Distortion energy (shape but not volume change) controls failure.Safe conditionFor plane stress reduces to
7Comparison between criteria Largest differences when principal strains have opposite signs
8Maximum difference between Tresca and von Mises Define stresses as 𝜎 1 , 𝜎 2 = 𝜎,𝛼𝜎 . For what 𝛼 do we get the maximum ratio between the two predictions of critical value of 𝜎? Can assume |𝛼|≤1. Why?Positive 𝛼. Tresca gives 𝜎= 𝑆 𝑦 . Von Mises leads to 𝜎 2 (1−𝛼+ 𝛼 2 )= 𝑆 𝑦 2 . Maximum for 𝛼=0.5, 𝜎= 𝑆 𝑦 =1.155 𝑆 𝑦Negative 𝛼. Tresca leads to 𝜎 1−𝛼 = 𝑆 𝑦 . Von Mises still same equation. Maximum ratio for 𝛼=-1. 𝜎 𝑇𝑟𝑒𝑠𝑐𝑎 =0.5 𝑆 𝑦 , 𝜎 𝑉𝑀 = 𝑆 𝑦 3Check!