# fiber composite materials – Hire Academic Expert

Google search “fiber composite materials” , fiber reinforced composite materials

Because fiber is usually much stronger than matrix, the fiber can be considered as “rigid”

Google search “fiber composite materials”

Google search “**rigid line inclusion**”

**Important introduction about rigid line inclusion:**

**https://en.wikipedia.org/wiki/Rigid_line_inclusion**

**Title of research: ****Mechanics of r****igid line inclusion in a matrix – simulation**

**Keywords:** Line inclusions, fiber composite materials, stress concentration

*y*

*c*

_{x }=0,_{xy }= 0

*h*

Matrix

*P*

u=0, _{xy }= 0

*x*

*a*

Inclusion

*a*

*h*

Fig.1.A rigid inclusion of length *a *in a medium of thickness 2*h* and width *c*, where and *P* is the prescribed forces on the left end of the medium.

Boundary conditions are:

On the left side: _{x }=0,_{xy }= 0,

On the right side: u=0, _{xy }= 0.

On the top surface: _{y}_{y }= 0, _{xy }= 0.

On the bottom surface: _{y}_{y }= 0, _{xy }= 0

Ansys

The rigid inclusion is to be modelled by “link” element in Ansys.

The matrix is to be modelled by “shell” element in Ansys.

Current limit:

Only for infinite h and c has been solved in exact form. Problem for finite h and c is more important.

Debonding mechanism between the inclusion and the matrix has not been fully understood.

You will – **Objective**:

1. Use Ansys model to study this problem

2. Obtain the dependence of the left inclusion tip displacement on the applied load for various values of a, c, and h.

3. Show the stress around the inclusion tips for various values of a, c, and h.

4. You will see that the stress at the inclusion tip is very high then other place. Accordingly, this high stress could result in the debonding of the inclusion from the matrix material. Therefore, you will study the debonding of the problem shown in Fig. 2.

_{x }=0,

_{xy }= 0

*y*

*c*

*h*

Matrix

*P*

u=0, _{xy }= 0

*x*

*a*

Inclusion

*d*

*a*

*h*

Fig.2. A rigid inclusion of length *a *in a medium of thickness 2*h* and width *c*, where and *P* is the prescribed forces on the left end of the medium. There is a debonding region between the inclusion and the matrix. The length of the debonding is *d*.

**Question:**

Identify the influence of h, c and a on the distribution of the stresses around the inclusion tip.

Explore the debonding mechanism between the inclusion and the matrix has not been fully understood.

**Methodology**

**We will use ****commercial**** softwar Ansys to simulate the inclusion/matrix system**

**E****xpected outcomes**

Provide a better understand of ****

Provide a design guideline for the reliable design of such material system.

**I. ****Background/Introduction**

The idea of rigid line inclusions is useful to stiffen materials. Rigid inclusions can be mathematically treated as an extremely thin but infinitely rigid reinforcement. The rigid inclusion model is very useful in the field of solid mechanics such as load diffusion [1] and material interface [2]. The most fundamental problem of the rigid inclusion was the anti-plane problem of a two-dimensional strip with a periodic array of inclusions that are normal to the strip faces [3]. The interaction of a rigid line inclusion with an elastic circular inclusion was studied and the singular stresses at the tips of the rigid inclusion and the stress field at the interface of the elastic inclusion were identified [4]. In addition, the interaction of inclusions with various geometries and layouts have been studied be means of the boundary element technique [5]. Notably, analytically solutions of pres-stressed elasticity were obtained and the shear bands were observed at the stiffer tips [6-8]. Rigid inclusion model was applied to study the stress concentration of materials at small scales with surface effects [9, 10]. In addition to the line, the plane problem of rigid circular-arc inclusions was studied and the expressions of the stresses were derived in closed form [11].

In engineering applications, many materials show non-homogeneity in properties. Therefore, a rigid line at a bi-material interface was studied in [2], and the anti-plane problems of rigid line inclusions at the interface between two dissimilar materials was studied in [12]. A layered system with an embedded rigid inclusion at the interface was investigated and the effects of geometry and mechanical parameters of the system were studied [13]. In [14], the solution of anti-plane elasticity for a periodic array of rigid line inclusions at the interfaces of the dissimilar and anisotropic materials was given. The stress intensities for a rigid line inclusion at the bi-material interface were examined by using the boundary element method [15]. Also obtained is the Green’s function method for a point force and the interaction between the dislocation and the interfacial elliptical rigid inclusion in a bi-material system [16]. The effect of rigid lines on the effective compliance of the composite system and the stress intensity factors at the inclusion tips were investigated in [17].

Understanding the effects of line inclusions on the mechanical properties of non-homogeneous and layered composites is very important for the reliable application of the materials. This paper develops an analytical model for the problem of multiple inclusions in a multilayered orthotropic medium under the anti-plane deformation. The medium is considered as a layered composite system with a number of layers. The solution of the entire system is obtained through introducing the continuity conditions of the displacements and stress at the interfaces. The solutions of strain and stress field are obtained and the strain intensity factors at the inclusion tips are given. In the numerical example, the model is applied to the analysis of functionally graded materials with any gradient parameter and layered composites with any number of layers. In addition to the problem of multiple parallel inclusions, the model of multiple collinear inclusions was also developed.