RD-E: 4801 Solid Spotweld Validation

Introduces how to model a solid element spotweld using /MAT/LAW83 + /FAIL/SNCONNECT and validate results using experiment data.

One element test to validate solid spotweld material and failure behavior.


Figure 1.
The following criteria are used to compare the results.
  • Maximum stress and force
  • Damage initiation displacement and failure displacement

Options and Keywords Used

Input Files

The input files used in this example include:
  • <install_directory>/hwsolvers/demos/radioss/example/48_solid_spotweld/one_solid_test/One_solid_element_validation_law83*

Model Description

The spotweld is represented by one solid element connected the upper and lower sheets using a tied contact.

Spotwelds are difficult to test independently. They are normally tested together with upper and lower surface parts. A KS2 test specimen is used in this example. Four loads are tested to characterize the mechanical behavior in tension, shear and moment; except for the peel test, the name of the test is based on the angle between the loading direction and the sheet metal.
  • Shear test (angle of load and sheet is 0°, below also named with 0° test)
  • Normal test (90° test)
  • Shear and normal combined tests (30° and 90° tests)
  • Peel test


Figure 2.
The spotweld thickness is half of the sum of the sheet metal thicknesses.(1) thickness= 2.0+1.5 2 =1.75 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG0bGaam iAaiaadMgacaWGJbGaam4Aaiaad6gacaWGLbGaam4CaiaadohacqGH 9aqpdaWcaaqaaiaaikdacaGGUaGaaGimaiabgUcaRiaaigdacaGGUa GaaGynaaqaaiaaikdaaaGaeyypa0JaaGymaiaac6cacaaI3aGaaGyn aaaa@4ADC@
Although physical spotwelds are normally cylindrical, they are modeled using a hex element with the same area as the physical cylindrical spotweld. A tied contact is used to attached the spotweld nodes to the upper and lower sheet metal.


Figure 3. Problem Description

Units: mm, ms, Kg, kN, GPa

The upper and lower sheet metal use /MAT/LAW36, with the following characteristics:
Material Properties
Initial density
7.85e-6 [Kg/mm3]
Young's modulus
210 [GPa]
Poisson ratio
0.3
Yield stress
0.370 [GPa]


Figure 4. Sheet Metal Stress Strain Curve

Simulation Iterations

The spotweld is modeled using the connection material /MAT/LAW83 and connection failure /FAIL/SNCONNECT.

In LAW83 the following parameters need to be determined and validated with the experimental data:
  • Yield curve, fct_ID1
  • Young's modulus
  • Maximum stress in normal and shear direction with R N ,  R S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbWaaS baaSqaaiaad6eaaeqaaOGaaiilaiaabccacaWGsbWaaSbaaSqaaiaa dofaaeqaaaaa@3C76@
  • Maximum stress for loads that combine normal and shear loading β
  • Maximum stress in moment (peel test) α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@3907@
In /FAIL/SNCONNECT, the beginning of displacement damage and final displacement failure needs to be determined and validated in the following experiments:
  • u ¯ 0 p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaaGimaaqaaiaadchacaWGSbaaaaaa@3B46@ and u ¯ f p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaamOzaaqaaiaadchacaWGSbaaaaaa@3B77@ in normal and shear direction with f 0 S MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOzamaaBa aaleaacaaIWaGaam4uaaqabaaaaa@38A0@ (fct_ID0S), f F S MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOzamaaBa aaleaacaaIWaGaam4uaaqabaaaaa@38A0@ (fct_IDFS), f 0 N MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOzamaaBa aaleaacaaIWaGaam4uaaqabaaaaa@38A0@ (fct_ID0N), and f F N MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOzamaaBa aaleaacaaIWaGaam4uaaqabaaaaa@38A0@ (fct_IDFN)
  • u ¯ 0 p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaaGimaaqaaiaadchacaWGSbaaaaaa@3B46@ and u ¯ f p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaamOzaaqaaiaadchacaWGSbaaaaaa@3B77@ in combined loading direction with β 0 ,  β f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGyda WgaaWcbaGaaGimaaqabaGccaGGSaGaaeiiaiabek7aInaaBaaaleaa caWGMbaabeaaaaa@3E04@
  • u ¯ 0 p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaaGimaaqaaiaadchacaWGSbaaaaaa@3B46@ and u ¯ f p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaamOzaaqaaiaadchacaWGSbaaaaaa@3B77@ in moment (peel test) with α 0 ,  α f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaaGimaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caWGMbaabeaaaaa@3E00@
LAW83 Yield Curve
In an experiment, force vs displacement in normal direction (90° test), tangent direction (0° test, shear) and in combined direction (30° and 60° tests) are measured. These results are converted to true stress vs plastic displacement curves. Next, the test results are normalized and used as the yield curve in LAW83 (input in fct_ID1). The stress should be normalized by maximum stress of shear test.


Figure 5. Normalized Yield Curve
LAW83 Young's Modulus

The Young’s modulus in LAW83 could also take Young’s modulus from true stress vs displacement curve of 0° test.

LAW83 Maximum Stress Validation

The maximum stress in the normal direction and in tangent direction is extracted from the 90° test and 0° shear test and input as R N , R S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbWaaS baaSqaaiaad6eaaeqaaOGaaiilaiaadkfadaWgaaWcbaGaam4uaaqa baaaaa@3BD3@ in LAW83.

The maximum stress in the combined direction is described by the parameter β which can be calculated using a fitting algorithm from the maximum stress in the 30° and 60° tests. The fitting is done using the following equation (ignoring α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@3907@ which is used in the peel test).(2) σ y = [ ( σ n R N f N ) β + ( σ s R S f S ) β ] 1 β MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadMhaaeqaaOGaeyypa0ZaamWaaeaadaqadaqaamaalaaa baGaeq4Wdm3aaSbaaSqaaiaad6gaaeqaaaGcbaGaamOuamaaBaaale aacaWGobaabeaakiabgwSixlGacAgadaWgaaWcbaGaamOtaaqabaaa aaGccaGLOaGaayzkaaWaaWbaaSqabeaacqaHYoGyaaGccqGHRaWkda qadaqaamaalaaabaGaeq4Wdm3aaSbaaSqaaiaadohaaeqaaaGcbaGa amOuamaaBaaaleaacaWGtbaabeaakiabgwSixlGacAgadaWgaaWcba Gaam4uaaqabaaaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacqaHYoGy aaaakiaawUfacaGLDbaadaahaaWcbeqaamaalaaabaGaaGymaaqaai abek7aIbaaaaaaaa@5867@


Figure 6. Yield Surface Fit Results for Combined Load Directions
In this example, check the /MAT/LAW83 parameters R N , R S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbWaaS baaSqaaiaad6eaaeqaaOGaaiilaiaadkfadaWgaaWcbaGaam4uaaqa baaaaa@3BD3@ with the fitted parameter β = 1.434 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGycq GH9aqpcaaIXaGaaiOlaiaaisdacaaIZaGaaGinaaaa@3DB5@ and no failure. This shows that the stress stays constant once it reaches the maximum stress. The maximum stress of 90° test, 0° test, 30° test and 60° test are close to experiment data.


Figure 7. Simulation versus Test Results
The maximum stress in the peel test is scaled from the maximum stress in the test using the parameter α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@3907@ from the following equation which does not include shear.(3) σ y = [ ( σ n R N f N ( 1 α sym ) ) β ] 1 β MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadMhaaeqaaOGaeyypa0ZaamWaaeaadaqadaqaamaalaaa baGaeq4Wdm3aaSbaaSqaaiaad6gaaeqaaaGcbaGaamOuamaaBaaale aacaWGobaabeaakiabgwSixlGacAgadaWgaaWcbaGaamOtaaqabaGc daqadaqaaiaaigdacqGHsislcqaHXoqycqGHflY1ciGGZbGaaiyEai aac2gaaiaawIcacaGLPaaaaaaacaGLOaGaayzkaaWaaWbaaSqabeaa cqaHYoGyaaaakiaawUfacaGLDbaadaahaaWcbeqaamaalaaabaGaaG ymaaqaaiabek7aIbaaaaaaaa@54FB@
This equation shows that the maximum stress in the peel test is scaled by ( 1 α sym ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca aIXaGaeyOeI0IaeqySdeMaeyyXICTaci4CaiaacMhacaGGTbaacaGL OaGaayzkaaaaaa@3FF7@ . Where s y m = sin ( A ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CaiaadM hacaWGTbGaeyypa0Jaci4CaiaacMgacaGGUbGaaiikaiaadgeacaGG Paaaaa@3EDB@ and A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaaaa@36BC@ is the angle between lower surface and upper surface of the solid element. This angle A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaaaa@36BC@ is hard to measure from experiment. To determine α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@3907@ , several validation simulations should be ran to determine the α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@3907@ value that matches the experimental peel test results. Since the maximum force peel test is 0.5* the maximum force in the 90°, a good starting value is α = 0.5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey ypa0JaaGimaiaac6cacaaI1aaaaa@3AC6@ . After a few iterations, you will find that α = 0.627 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey ypa0JaaGimaiaac6cacaaI2aGaaGOmaiaaiEdaaaa@3C44@ results in a maximum force in peel simulation that matches the experiment data.


Figure 8. Simulation and Experimental Results for 90° and Peel Loads
Spotweld Failure (/FAIL/SNCONNECT)
After validating the maximum stress with LAW83, the spotweld failure needs to be validated using the failure model /FAIL/SNCONNECT. In this failure model, you need the displacement value where damage begins u ¯ 0 p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaaGimaaqaaiaadchacaWGSbaaaaaa@3B46@ and displacement at failure u ¯ f p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaamOzaaqaaiaadchacaWGSbaaaaaa@3B77@ from the experiment.


Figure 9. Stress vs Displacement Plot
  • Spotweld failure in 90° (normal) and 0° (shear) test
    Input the displacement where damage begins u ¯ 0 p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaaGimaaqaaiaadchacaWGSbaaaaaa@3B46@ and displacement at failure u ¯ f p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaamOzaaqaaiaadchacaWGSbaaaaaa@3B77@ from the 90° test into functions ( f 0 N MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOzamaaBa aaleaacaaIWaGaam4uaaqabaaaaa@38A0@ (fct_ID0N) and ( f F N MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOzamaaBa aaleaacaaIWaGaam4uaaqabaaaaa@38A0@ (fct_IDFN) and from test into functions ( f 0 S MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOzamaaBa aaleaacaaIWaGaam4uaaqabaaaaa@38A0@ (fct_ID0S) and f F S MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOzamaaBa aaleaacaaIWaGaam4uaaqabaaaaa@38A0@ (fct_IDFS). Since there is no rate effect data, the curves will be constant.


    Figure 10. Beginnining and Failure Damage Displacements
    Using these values in a simulation, the beginning damage displacement and failure displacement match very well to the 0° test results. However, the simulation does not match very well to the 90° test. This is due to the deformation of upper and lower sheet metal. In the 0° test, the sheet metal barely deforms.


    Figure 11. Simulation with Damage and Experimental Results. 0° and 90° tests
    Using the displacement of the sheet metal from the simulation results, the sheet metal displacement is subtracted from the u ¯ 0 p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaaGimaaqaaiaadchacaWGSbaaaaaa@3B46@ and u ¯ f p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaamOzaaqaaiaadchacaWGSbaaaaaa@3B77@ of the 90° test. After doing this, the force displacement curves in the simulation match the test.


    Figure 12. Improved Failure Results
  • Spotweld Failure in Combined Tests
    The beginning and failure damage in the 30° and 60° tests (combined normal and shear loading) can be defined using the parameters β 0 ,   β f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGyda WgaaWcbaGaaGimaaqabaGccaGGSaGaaeiiaiabek7aInaaBaaaleaa caWGMbaabeaaaaa@3E04@ in the following equations, which do not consider α 0 ,   α f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaaGimaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caWGMbaabeaaaaa@3E00@ which are for peel test.(4) 1 = [ ( u ¯ 0 , n p l f 0 N ) β 0 + ( u ¯ 0 , s p l f 0 S ) β 0 ] 1 β 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiabg2 da9maadmaabaWaaeWaaeaadaWcaaqaaiqadwhagaqeamaaDaaaleaa caaIWaGaaiilaiaad6gaaeaacaWGWbGaamiBaaaaaOqaaiGacAgada WgaaWcbaGaaGimaiaad6eaaeqaaaaaaOGaayjkaiaawMcaamaaCaaa leqabaGaeqOSdi2aaSbaaWqaaiaaicdaaeqaaaaakiabgUcaRmaabm aabaWaaSaaaeaaceWG1bGbaebadaqhaaWcbaGaaGimaiaacYcacaWG ZbaabaGaamiCaiaadYgaaaaakeaaciGGMbWaaSbaaSqaaiaaicdaca WGtbaabeaaaaaakiaawIcacaGLPaaadaahaaWcbeqaaiabek7aInaa BaaameaacaaIWaaabeaaaaaakiaawUfacaGLDbaadaahaaWcbeqaam aalaaabaGaaGymaaqaaiabek7aInaaBaaameaacaaIWaaabeaaaaaa aaaa@573B@ (5) 1 = [ ( u ¯ f , n p l f F N ) β f + ( u ¯ f , s p l f F S ) β f ] 1 β f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiabg2 da9maadmaabaWaaeWaaeaadaWcaaqaaiqadwhagaqeamaaDaaaleaa caWGMbGaaiilaiaad6gaaeaacaWGWbGaamiBaaaaaOqaaiGacAgada WgaaWcbaGaamOraiaad6eaaeqaaaaaaOGaayjkaiaawMcaamaaCaaa leqabaGaeqOSdi2aaSbaaWqaaiaadAgaaeqaaaaakiabgUcaRmaabm aabaWaaSaaaeaaceWG1bGbaebadaqhaaWcbaGaamOzaiaacYcacaWG ZbaabaGaamiCaiaadYgaaaaakeaaciGGMbWaaSbaaSqaaiaadAeaca WGtbaabeaaaaaakiaawIcacaGLPaaadaahaaWcbeqaaiabek7aInaa BaaameaacaWGMbaabeaaaaaakiaawUfacaGLDbaadaahaaWcbeqaam aalaaabaGaaGymaaqaaiabek7aInaaBaaameaacaWGMbaabeaaaaaa aaaa@5852@
    Taking u ¯ 0 p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaaGimaaqaaiaadchacaWGSbaaaaaa@3B46@ and u ¯ f p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaamOzaaqaaiaadchacaWGSbaaaaaa@3B77@ from experiment data:


    Figure 13. Test Results - 30° and 60°
    Using the results from the 30° and 60° tests, the β 0 = 2.389 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGyda WgaaWcbaGaaGimaaqabaGccqGH9aqpcaaIYaGaaiOlaiaaiodacaaI 4aGaaGyoaaaa@3EAF@ and β f = 2.249 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGyda WgaaWcbaGaamOzaaqabaGccqGH9aqpcaaIYaGaaiOlaiaaikdacaaI 0aGaaGyoaaaa@3EDB@ values are calculated using an equation fitting routine.


    Figure 14. Damage and Failure Surface Fit


    Figure 15. Results Initial Beta Parameter Fitting
    Using the calculated fitted parameters β 0 ,   β f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGyda WgaaWcbaGaaGimaaqabaGccaGGSaGaaeiiaiabek7aInaaBaaaleaa caWGMbaabeaaaaa@3E04@ , the simulation shows that the start of the damage does not match the experimental data. Similar to the 90° test, the deformation of sheet metal needs to be excluded from the damage displacements. The sheet metal displacement from the simulation is subtracted from the damage displacement and new parameters β 0 = 3.2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGyda WgaaWcbaGaaGimaaqabaGccqGH9aqpcaaIZaGaaiOlaiaaikdaaaa@3D2A@ and β f = 3.721 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGyda WgaaWcbaGaamOzaaqabaGccqGH9aqpcaaIZaGaaiOlaiaaiEdacaaI YaGaaGymaaaa@3ED7@ are calculated using the fitting algorithm.


    Figure 16. Damage and Failure Surface Fit


    Figure 17. Validation - 30° and 60° Tests

    Using the updated β 0 ,   β f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGyda WgaaWcbaGaaGimaaqabaGccaGGSaGaaeiiaiabek7aInaaBaaaleaa caWGMbaabeaaaaa@3E04@ parameters, the beginning of the damage better matches the experiment data.

  • Spotweld Failure in Peel Test

    To correctly simulate the moment loads that occur in the peel test, the α 0 ,   α f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaaGimaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caWGMbaabeaaaaa@3E00@ scale factor parameters must be calculated.

    If the shear terms are ignored, the beginning and failure damage is represented as:(6) 1 = u ¯ 0 , n p l f 0 N ( 1 α 0 s y m ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiabg2 da9maalaaabaGabmyDayaaraWaa0baaSqaaiaaicdacaGGSaGaamOB aaqaaiaadchacaWGSbaaaaGcbaGaciOzamaaBaaaleaacaaIWaGaam OtaaqabaGcdaqadaqaaiaaigdacqGHsislcqaHXoqydaWgaaWcbaGa aGimaaqabaGccqGHflY1caWGZbGaamyEaiaad2gaaiaawIcacaGLPa aaaaaaaa@4AF4@ (7) 1 = u ¯ f , n p l f F N ( 1 α f s y m ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiabg2 da9maalaaabaGabmyDayaaraWaa0baaSqaaiaadAgacaGGSaGaamOB aaqaaiaadchacaWGSbaaaaGcbaGaciOzamaaBaaaleaacaWGgbGaam OtaaqabaGcdaqadaqaaiaaigdacqGHsislcqaHXoqydaWgaaWcbaGa amOzaaqabaGccqGHflY1caWGZbGaamyEaiaad2gaaiaawIcacaGLPa aaaaaaaa@4B67@
    The ( 1 α 0 sym ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca aIXaGaeyOeI0IaeqySde2aaSbaaSqaaiaaicdaaeqaaOGaeyyXICTa ci4CaiaacMhacaGGTbaacaGLOaGaayzkaaaaaa@40E7@ and ( 1 α f sym ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca aIXaGaeyOeI0IaeqySde2aaSbaaSqaaiaadAgaaeqaaOGaeyyXICTa ci4CaiaacMhacaGGTbaacaGLOaGaayzkaaaaaa@4118@ terms scale the normal term in the equation. As done before for LAW83, the α 0 ,   α f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaaGimaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caWGMbaabeaaaaa@3E00@ terms can be determined using the simulation and optimization or trial and error to match the peel test results. Starting with α 0 = 0.5 ;   α f = 0.5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaaicdaaeqaaOGaeyypa0JaaGimaiaac6cacaaI1aGaai4o aiaabccacqaHXoqydaWgaaWcbaGaamOzaaqabaGccqGH9aqpcaaIWa GaaiOlaiaaiwdaaaa@4309@ and the knowledge that increasing these terms decreases the u ¯ 0 p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaaGimaaqaaiaadchacaWGSbaaaaaa@3B46@ and u ¯ f p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaamOzaaqaaiaadchacaWGSbaaaaaa@3B77@ values, you determine that the parameters α 0 = 1.2 ;   α f = 1.3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaaicdaaeqaaOGaeyypa0JaaGymaiaac6cacaaIYaGaai4o aiaabccacqaHXoqydaWgaaWcbaGaamOzaaqabaGccqGH9aqpcaaIXa GaaiOlaiaaiodaaaa@4306@ (peel test 2) result in u ¯ 0 p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaaGimaaqaaiaadchacaWGSbaaaaaa@3B46@ and u ¯ f p l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWG1bGbae badaqhaaWcbaGaamOzaaqaaiaadchacaWGSbaaaaaa@3B77@ values that match the experimental peel test data.


    Figure 18. Validation - Peel Test

Results

With a minimum of 4 different experimental tests, input data for /MAT/LAW83 + /FAIL/SNCONNECT can be validated for use with solid brick element spotwelds.

Using a KS2 test specimen, a 0° test, 90° test, peel test and at least one combined loading (30, 45 or 60 degree) test is needed. Since there can be variations in the test data, it is better to have multiple test results for each test.

If upper and lower sheets deformed during the test, the simulations results can be used to modify the damage displacements during the validation of the spotweld failure displacement in /FAIL/SNCONNECT.