PSI - Issue 61

T. Stoel et al. / Procedia Structural Integrity 61 (2024) 206–213 T. Stoel et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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3

(b) Fiber orientation relative to the cutting line 1 = 0 ° 2 = 90 ° 1 = 45 ° 2 = 45 ° 1 = 22.5 ° 2 = 67.5 °

(a) Near-net-shape blanking

b

Punch

PU = B CP

A

1

1

1

Blank holder

2

2

2

2

2

2

A

1

1

1

Laminate

CP

Shear zone

Punch

Laminate

Fiber

Die

(c) Fiber volume fraction f = 60 % A-A

f = 70 % A-A

Fiber

Counter punch

Die clearance = 0.005

Matrix

Figure 1: Schematic illustration of near-net-shape blanking (a), fiber orientation relative to the cutting line (b) and fiber volume fraction (c) Legend: b – Blanking velocity; BH – Blank holder force; CP – Counter force; PU – Punch force; B – Blanking force; – laminate thickness The influence of the fiber orientation relative to the cutting line on the blanking force was investigated using three different orientations 1,2 = {0 ° , 90 ° }, 1,2 = {22.5 ° , 67.5 ° } and 1,2 = {45 ° , 45 ° } (Figure 1b). A fiber volume fraction of f = 60 % and f = 70 % was evaluated which determines the share of fiber in the whole laminate (Figure 1c). Furthermore, the influence of the applied process forces on the resulting blanking force was analyzed by using a set of low ( BH− and CP− ) and high values ( BH+ and CP+ ) for blank holder and counter force (see Table 3). 2.2. Material modeling The material behavior of CFRP can be characterized as elastic-brittle. Until the onset of damage, the material behaves in a purely elastic manner. When material damage occurs, the ideal-elastic range is left, and the material behaves increasingly brittle. According to this modeling, the described material behavior is realized by an increasing reduction of the stiffness, which is expressed in the constitutive equation by a fourth-order damage tensor : ̂ = ∙ = ∙ ∙ (1) where ̂ is the effective stress tensor, is the undamaged stiffness tensor and is the strain tensor. The onset of damage is determined by a damage initiation criterion and the reduction of stiffness by a damage evolution law. Furthermore, the composite character of the laminate as well as the stress state is considered which leads to the usage of four damage modes : fiber tension t , fiber compression c , matrix tension t and matrix compression c for both damage initiation criterion and damage evolution law. For the damage initiation of the fiber tension mode, a modified version of the criterion by Hashin (1980) and for fiber compression mode a simple maximum stress formulation was used. Damage initiation of the matrix modes was realized by Pucks’ criteria (Knops (2008)). Damage evolution was achieved due to a linear degradation law of the stiffness by Lapczyk (2007). For more information on the formulation of the criteria and the used parameterization, refer to Shirobokov et al. (2018). Nevertheless, some specific adjustments in the modeling have been made. First of all, for fiber tension mode in damage initiation the original criterion by Hashin (1980) with a shear contribution factor of = 1 was used. Thus, the shear stresses exert a maximum influence on the damage initiation parameter for fiber tension mode. Second, the element deletion and as a result laminate failure is also determined by the damage variable of the fiber tension mode ft , analogous to the studies by Shirobokov et al. (2018), however element deletion is already triggered at ft = 0.97. This prevents excessive element distortion caused by the degressive increase of the damage evolution variables.