PSI - Issue 57

Ahmad Qaralleh et al. / Procedia Structural Integrity 57 (2024) 649–657 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Table 2 Characteristic parameters for describing the stress-strain curve from the incremental step test.

Cyclic strength coefficient K’ [MPa]

Cyclic strength exponent n’ [-]

Cyclic yield stress [MPa]

Strain amplitude [%]

Elastic modulus [GPa]

0.8 0.8 0.6 0.6 0.4

192 193 191 195 193

1975 1852 2173 2157 3358

0.1625 0.1592 0.1760 0.1740 0.2140

719 690 728 733 888

4.2. Comparison of material behavior at constant and variable amplitudes

Comparing the stress-strain behavior under cyclic loading with constant and variable amplitudes gives valuable information on the material response under different load amplitudes. Also, it could give reliable knowledge of the sliding behavior of the material (Wagener & Schatz, 2005). In the case of materials with a wavy sliding character, the stress-strain behavior differs between constant and variable amplitudes since a different dislocation mechanism act at high loads than at low ones. This is based on the cyclic stress-strain curves obtained from an Incremental Step Test with a maximum strain value of ε a,max = 0.8%, as shown in Fig. 7/a. The cyclic stress-strain behavior at half the failure life closely resembles the initial loading. Differences between constant and variable amplitude loading occur during the transition from linear-elastic to elastic-plastic behavior. The transition to elastic-plastic behavior in cyclic loading with constant amplitudes occurs at slightly higher stresses, but the stress-strain curve in the elastic-plastic range is flatter. Fig. 7/b shows that by reducing the maximum strain amplitude to ε a,max =0.6%, the difference in material behavior between constant and variable amplitude loading decreases, and further reduction to ε a,max =0.4% leads to an agreement in the cyclic material behavior as it is mostly behaving elastically, as shown in Fig. 7/c. a.) b.) c.)

CAL E' = 192.5 GPa K' = 1463,7 n' = 0.1074 R p0,2 ' = 751 MPa R e = -1

CAL E' = 192.5 GPa K' = 1463.7 n' = 0.1074 R p0,2 ' = 751 MPa R e = -1

CAL E' = 192.5 GPa K' = 1463.7 n' = 0.1074 R p0,2 ' = 751 MPa R e = -1

1000

1000

1000

800

800

800

200 Stress Amplitude s a [MPa] 400 600

200 Stress Amplitude s a [MPa] 400 600

200 Stress Amplitude s a [MPa] 400 600

E* = 192.6 GPa K* = 3358 MPa n* = 0.214 R p0,2 * = 888 MPa R e = -1 e a,t,max = 0.4% Incremental Step Test

E* = 190.9 GPa K* = 2173 MPa n* = 0.176 R p0,2 * = 728 MPa R e = -1 e a,t,max = 0.6% Incremental Step Test

E* = 192 GPa K* = 1975 MPa n* = 0.1625 R p0,2 * = 719 MPa R e = -1 e a,t,max = 0.8% Incremental Step Test

0

0

0

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

Strain Amplitude e a,t [%]

Strain Amplitude e a,t [%]

Strain Amplitude e a,t [%]

Fig. 7 Comparison of the cyclic stress-strain curves determined with constant amplitude loading (CAL) and the incremental step test. a.) ε a,t = 0.8%; b.) ε a,t = 0.6%; c.) ε a,t = 0.4% 5. Numerical Evaluation A finite element (FE) model was developed to replicate the steering knuckle geometry utilized in the experimental testing. The model was constructed and processed using Abaqus software, paying attention to meshing and boundary conditions in the radius as highlighted in Fig. 8 to obtain precise results. Fig. 8 provides an overview of the model's geometry and mesh as well as the hot spot region based on the FE analysis. Furthermore, the applied loads on the model were adjusted to reflect the real operating conditions of the steering knuckle in a commercial vehicle. Both