PSI - Issue 41

Peter Zobec et al. / Procedia Structural Integrity 41 (2022) 208–214 Peter Zobec / Structural Integrity Procedia 00 (2022) 000–000

209

2

Table 1. Strain-life test results.

Specimens at level Strain amplitude ϵ a [%] Strain rate ˙ ϵ [% / s]

Cycles to failure N f 18768, 10192,11683 2401, 2342, 1647, 2932

3 4 4 1

0.25

1.25

0.5

0.3 0.4

1

606, 760, 705, 492

1.5

0.15

101

initiation and growth. CHE is a process of achieving plastic radial flow through various means on the walls of the hole. This is often achieved by pulling a mandrel of slightly larger radius through the hole. When the mandrel is removed, a field of compressive residual stress (RS) is left on the surface of the hole. Typically, the e ff ect of RS on fatigue stress is thought to be similar to that of mean stress, with mean compressive stress lowering the stress amplitude of the fatigue load and thus extending fatigue life. The reverse is true for the mean tensile stress. This e ff ect of CHE -fatigue interaction is well documented [13–15]. However, we must be aware of the essential di ff erence between mean and RS. Mean stress results from an external fatigue load, while RS is internally in self-equilibrium. If the fatigue load has a constant amplitude, the mean stress is also constant. RS interacts with the fatigue load and may relax when the combined e ff ect of RS and the loading stress reaches yield. As the fatigue crack develops and grows, it also interacts with the RS field. It has been shown that the compressive stress RS has a closing e ff ect on the crack, slowing its growth. When the crack reaches the tensile field RS, the crack accelerates. [16–19]. The mechanical background of fatigue crack growth modelling is fracture mechanics. Here, the e ff ect of RS is modelled by the concept of e ff ective stress intensity. In most studies, the field RS has been assumed to remain constant and una ff ected by both fatigue loading and the presence of a crack. The reason for this is the lack of modelling techniques in (linear elastic) fracture mechanics, since the relaxation of RS is governed by a nonlinear material model that must also account for the Baushinger e ff ect of reverse yielding. Here we look at CHE, RS and fatigue crack growth from a di ff erent perspective. Most studies on CHE focused on preventing fatigue crack growth on the surface of the hole. The objective of this study is to investigate the fatigue crack growth of a crack originating from and growing toward a CHE hole. The fatigue loading that a ff ects the crack growth also a ff ects or relaxes the condition of RS near the hole. This study presents results based on numerical simulations using the finite element method (FEM), for which material models for S235 structural steel were used.

2. Materials and methods

2.1. Material models

A series of laboratory tests were conducted to gain insight into the cyclic properties of S235 steel. The research focused on fatigue properties at low cycles. The results are shown in the table 1 and the strain-life curve is shown in the figure 1. The strain-life curve is fitted with parameters σ f = 551 . 4 MPa , ϵ f = 0 . 3109, b = − 0 . 06493, c = − 0 . 5843, and E = 213 . 7 GPa .

σ f E

N b

c f

f + ϵ f N

(1)

ϵ a =

The combined non-linear kinematic and isotropic hardening model with three back-stress evolution was used to model the material. The model parameters are given in table 1. [20] To simulate fatigue crack growth, a novel approach was used as described in [21]. A Morrow mean stress correction model was used to model the e ff ect of RS on fatigue state and crack propagation.

σ f − σ m E

N b

c f

f + ϵ f N

(2)

ϵ a =

2.2. Fatigue and fatigue crack growth algorithm

The ”YAA2FCG” [21] approach was used to simulate both fatigue and crack initiation and growth. Since the studied area FEM starts without crack, a lot of computational time would be required to simulate all cycles to crack