OS-V: 1220 Damage Initiation and Evolution Study, Notched Sample

A notched sample with CQUAD4 elements is subjected to a quasi-static enforced displacement with one end fixed.

The goal is to study the damage initiation and evolution from the results and correlate them with the inputs provided in DMGINI and DMGEVO Bulk Data Entries using an explicit dynamic analysis. For MATF/INIEVO definition, refer to MATF and OS-V: 1220 Damage Initiation and Evolution Study, Notched Sample.
Figure 1. Notched Sample


Figure 2. Displacement and Constraint Applied


Model Files

Before you begin, copy the file(s) used in this problem to your working directory.

Benchmark Model

The finite element shell model discretized with CQUAD4 elements, as shown in Figure 1, represents a notched sample subjected to a quasi-static enforced displacement. A vertical displacement is applied on the center node of the top edge as shown in Figure 2. MATF/INIEVO definition is shown in Figure 3. Equivalent plastic strain at damage onset is defined at two stress states (triaxiality). Damage initiation rate is independent. Damage evolution is based on plastic displacement and the evolution shape is linear.
Figure 3. DMGINI and DMGEVO Definitions


Material

Elastic-plastic Material Properties
Young's modulus
192400
Poisson's ratio
0.3
Density
7.85E-06
Plastic Properties
TABLEG entries for stress strain curve
Strain Stress
0.0 100.0
0.015 200.0
Yield function criterion
Von Mises
Hardening rule
1 (Isotropic hardening)
Type of strain
1 (Plastic strain used on X-axis)

Results

Damage onset takes place on element 2911 at t = 0.585s, when damage initiation Index reaches 1.0. Damage initiation index, stress triaxiality, and equivalent plastic strain at t = 0.585 for the entire model are presented in Figure 4. Additionally, equivalent plastic strain at the end of the analysis is shown in the same figure. At t = 0.585s, stress triaxiality on element 2911 is 0.387. The two-point DMGINI table defines equivalent plastic strain as:

ε D p l = − 0.0075 * S t r e s s   T r i a x i a l i t y + 0.03 MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqyTdu2damaaDaaaleaapeGaamiraaWdaeaapeGaamiCaiaadYga aaGccqGH9aqpcqGHsisldaqadaWdaeaapeGaaGimaiaac6cacaaIWa GaaGimaiaaiEdacaaI1aGaaiOkaiaadofacaWG0bGaamOCaiaadwga caWGZbGaam4CaiaacckacaWGubGaamOCaiaadMgacaWGHbGaamiEai aadMgacaWGHbGaamiBaiaadMgacaWG0bGaamyEaaGaayjkaiaawMca aiabgUcaRiaaicdacaGGUaGaaGimaiaaiodaaaa@5857@

With stress triaxiality of 0.387, equivalent plastic strain at damage onset is 0.027, which matches the value of the analysis (Results C). The relationship between the plastic displacement (0.020 in DMGEVO) and equivalent plastic strain is:

u f = L ε f p l − ε D p l MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyDa8aadaWgaaWcbaWdbiaadAgaa8aabeaak8qacqGH9aqpcaWG mbWaaeWaa8aabaWdbiabew7aL9aadaqhaaWcbaWdbiaadAgaa8aaba WdbiaadchacaWGSbaaaOGaeyOeI0IaeqyTdu2damaaDaaaleaapeGa amiraaWdaeaapeGaamiCaiaadYgaaaaakiaawIcacaGLPaaaaaa@468A@

Where L is the characteristic length, which is for shell elements. The area of the element is 0.3876, and consequently, L = 0.623. Equivalent plastic strain at ultimate damage can be solved as:

ε f pl = 0.020 0.623 +0.027=0.059 MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqyTdu2damaaDaaaleaapeGaamOzaaWdaeaapeGaamiCaiaadYga aaGccqGH9aqpdaWcaaWdaeaapeGaaGimaiaac6cacaaIWaGaaGOmai aaicdaa8aabaWdbiaaicdacaGGUaGaaGOnaiaaikdacaaIZaaaaiab gUcaRiaaicdacaGGUaGaaGimaiaaikdacaaI3aGaeyypa0JaaGimai aac6cacaaIWaGaaGynaiaaiMdaaaa@4CC2@

This matches the value of the analysis. The value of the equivalent plastic strain is recorded at the time the element is eroded and remains the same for the rest of the analysis (Results D).
Figure 4. Results. A - Damage Initiation Index at t=0.585, B - Stress Triaxiality at t=0.585, C - Equivalent Plastic Strain at t=0.585, D - Equivalent Plastic Strain at t=1.0


Figure 5. Element 2911 Specific Results. Stress vs equivalent plastic strain (left); damage initiation index, damage index, stress triaxiality, and equivalent plastic strain (scaled by x10 for visualization) as function of time (right)


Element 2911 specific results are shown in Table 1. Stress triaxiality and strain rate do not influence the damage evolution phase.
Table 1. Element 2911 Specific ResultsDamage initiation index, damage index, stress triaxiality, and equivalent plastic strain as function of time
Time 0.585 0.715 1.0*
Damage Initiation Index 1.0 1.0 1.0
Damage Index 0.01 1.0 1.0
Stress Triaxiality 0.387 - 0.0
Equivalent Plastic Strain 0.027 0.059 0.059

* Element eroded