Calculation of damage accumulation taking into account changes in material characteristics

. One of the important issues in the study of composite materials are microdefects and their accumulation in the binder. Cracks that occur in the transverse directions of the layers are considered to be the most common macrodefect. During cracking, the elastic modulus and shear modulus decrease. This article discusses the issue of obtaining calculation formulas that take into account the accumulation of damage, taking into account cracks in the layers and interlayer cracks on the example of the wing joint with the center section.


Introduction
During long-term operation of composite materials, a decrease in elastic modulus and shear modulus is observed due to the destruction of the binder. Joint nodes are one of the important elements of aircraft structures. Therefore, when calculating the cyclic load, it is important to take into account the accumulation of damage.
The relevance of this study is the possibility of taking into account the accumulation of damage in the joints of aircraft structures.
In this article, the calculation of damage accumulation is shown using the example of the wing joint with the center section.
The purpose of this study is to obtain calculation formulas that take into account the accumulation of damage, taking into account the interlayer crack.
The objectives of this study are: 1. Modeling of degradation properties of layered composites. 2. Prediction of changes in characteristics with increasing damage during cyclic loading.
Currently, a large number of studies are being carried out on the degradation of mechanical characteristics.
In [1], effective mechanical characteristics were obtained and the fracture in the layers was calculated and the interaction of cracks on the material characteristics was taken into account. With the same crack densities and different relative distances between cracks, the modulus of elasticity decreases. With tensile stresses close to destructive, the interaction between cracks will lead to a greater decrease in the modulus of elasticity.
The most common microdefects are transverse cracks in layers of composite material. Questions about the reduction of elastic modulus and shear during cracking of transverse layers are considered in [2][3][4].
The process of crack formation in transverse layers of composite material under static and cyclic loading is described in [5][6][7].
The process of damage accumulation in composite materials depends on the direction of reinforcement. This issue is considered in the works [8][9].
In [17], the stratification along rectilinear free edges of layered composites is considered. Also in [17], an experimental method for determining the interlayer normal stress in the median plane of a layered composite using strain gauges is described, and a method for analytical prediction of the onset of stratification on the interface under the action of normal and tangential stresses is described. As a result, it was found that the accuracy of predicting the beginning of stratification decreases when tangential stresses exceed normal; delamination usually occurs along the same interface where the interlayer tensile stress reaches a maximum.

Calculation model
As an example, this article considers the joint of the wing with the center section. Using the damage accumulation calculation algorithm described in [18,19], changes in elastic and shear modulus were obtained. Figure 1 shows an example of the location of a transverse crack that occurs at the junction node. These cracks can occur in the structures of composite materials under cyclic and quasi-static loads. Consider the case for the structure of a composite material [0°,±45°,90°]. First of all, the stiffness for a given structure of an intact material is determined. Indexes (1), (2) and (3) correspond to layers with stacking angles 0°,±45°,90.
Stiffness 11 12 22 ,, B B B are determined according to the formula: Next, we define an effective module for this structure: The next step is to determine the deformations from the operating loads. The stresses of the entire package and in each layer are determined by deformations.
After determining the deformations and stresses, using the relations that take into account the degradation of properties in the layers, we obtain the degradation of the effective modules of the material.
We show a change in the effective characteristics for the structure (0°, ±45°,90°). For this case, we consider that: (2) 11 (2) 12 12 (1 ), The upper index 2 indicates the transverse layer. According to [19], we obtain the following values for the coefficients:     Figure 4 shows the change in the shear modulus taking into account the initial defect for the structure [0°, ±45°,90°].

Conclusions
In this article, the case of damage accumulation for the structure of a composite material is considered (0°, ±45°,90°) taking into account the interlayer crack. Calculation formulas were obtained that make it possible to predict the change in characteristics with increasing damage and taking into account the interlayer crack in the joint. On the example of the wing joint with the center section, the dependences of the elastic modulus and shear modulus are obtained, taking into account the existing initial defect from the interlayer crack.