Fatigue Assessment Methods

In SimSolid, uniaxial and multiaxial fatigue analysis using SN (stress-life) and EN (strain-life) approach is supported.

Models with uniaxial loads consist of loading in only one direction and result in one principal stress. In Uniaxial Fatigue Analysis, SimSolid converts the stress tensor to a scalar value using user-defined combined stress method (signed von Mises, maximum principal, absolute max principal, signed maximum shear stress, and critical plane).

For critical plane stress, nominal stress resolved at each plane 𝜃 is calculated by:

σ = σ x ( cos 2 θ ) + σ y ( sin 2 θ ) + 2 σ x y ( cos θ sin θ ) θ = 0 , 10 , 20 , 30......170   degrees , MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqaHdp WCcqGH9aqpcqaHdpWCdaWgaaWcbaGaamiEaaqabaGcdaqadaqaaiGa cogacaGGVbGaai4CamaaCaaaleqabaGaaGOmaaaakiabeI7aXbGaay jkaiaawMcaaiabgUcaRiabeo8aZnaaBaaaleaacaWG5baabeaakmaa bmaabaGaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaaaOGaeq iUdehacaGLOaGaayzkaaGaey4kaSIaaGOmaiabeo8aZnaaBaaaleaa caWG4bGaamyEaaqabaGcdaqadaqaaiGacogacaGGVbGaai4CaiabeI 7aXjGacohacaGGPbGaaiOBaiabeI7aXbGaayjkaiaawMcaaaqaaiab eI7aXjabg2da9iaaicdacaGGSaGaaGymaiaaicdacaGGSaGaaGOmai aaicdacaGGSaGaaG4maiaaicdacaGGUaGaaiOlaiaac6cacaGGUaGa aiOlaiaac6cacaaIXaGaaG4naiaaicdacaaMe8Uaaeizaiaabwgaca qGNbGaaeOCaiaabwgacaqGLbGaae4CaiaacYcaaaaa@76D1@

SimSolid expects the number of planes as input, which are converted to equivalent 𝜃 using the following equation:

θ = 180 n − 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiUdeNaey ypa0ZaaSaaaeaacaaIXaGaaGioaiaaicdaaeaacaWGUbGaeyOeI0Ia aGOmaaaaaaa@3D95@

In Multiaxial Fatigue Analysis, SimSolid uses the stress tensor directly to calculate damage. Multiaxial Fatigue Analysis theories assume that stress is in the plane-stress state.

In multiaxial fatigue analysis, SimSolid always searches for the most damaging plane by assessing damage using tensile crack damage model and shear crack damage model. At the end of search, SimSolid reports damage at the most damaging plane which is the critical plane.

Critical Plane Approach

Experiments show that cracks nucleate and grow on specific planes known as critical planes. The Critical Plane Approach captures the physical nature of damage in its damage assessment process.

Depending on the material and stress states, the critical planes can be either maximum shear planes or maximum tensile stress planes. Therefore, to assess damage from multiaxial loads, two separate damage models are required. One is for crack growth due to shear, and the other is for crack growth due to tension.
Figure 1. Cracks driven by Shear and Tensile Stress


Figure 2. Cyclic, Torsion, Shear Strain, Tensile Strain, Shear and Tensile damage


You can use any damage model the critical plane approach. The damage models require a search for the most damaging plane. There are two possible damaging (or failure) modes. One is tensile crack growth, which occurs on planes that are perpendicular to the free surface. The angle θ is the angle that a crack is observed on the surface relative to the σx direction. The second failure system is shear crack growth, which occurs on planes oriented 45 degrees to the surface. Both in-plane and out-of-plane shear stresses are considered on this plane. θ can take on any value on the surface. The shear stress τA is an in-plane shear stress and causes microcracks to grow along the surface. The maximum out-of-plane shear, τB occurs on a plane that is oriented at 45 degrees from the free surface and causes microcracks to grow into the surface.
Figure 3. In-Plane Shear Stress and Normal Stress at 90 Degree Plane; In-Plane and Out-of-Plane Shear Stress at a 45 Degree Plane