In this paper, the evaluations of metal ablation processes under high temperature, i.e., the Al plate ablated by a laser and a heat carrier and the reactor pressure vessel ablated by a core melt, are studied by a novel peridynamic method. Above all, the peridynamic formulation for the heat conduction problem is obtained by Taylor’s expansion technique. Then, a simple and efficient moving boundary model in the peridynamic framework is proposed to handle the variable geometries, in which the ablated states of material points are described by an additional scalar field. Next, due to the automatic non-interpenetration properties of peridynamic method, a contact algorithm is established to determine the contact relationship between the ablated system and the additional heat carrier. In addition, the corresponding computational procedure is listed in detail. Finally, several numerical examples are carried out and the results verify the validity and accuracy of the present method.

The metal ablation under high temperature is ubiquitous in many engineering problems, such as the welding of the steels, the laser strengthening of the aluminum alloys, and the ablation of the reactor pressure vessels (RPVs) caused by a core melt in serious accidents, etc. Importantly, the properties of these metal materials and structures may change dramatically after the thermal ablation, which could eventually improve or reduce the levels of strength, stability, workability, safety of the materials and structures, and so on. Therefore, it is very essential to study metal ablation problems. During the past several decades, studies of metal ablation problems have been conducted by many researchers from the aspects of theories, experiments and simulations. For instance, the characteristics of the thermal ablation, such as the microtopologies, the thermal boundaries and the thermal damages, were investigated by the experimental and numerical methods [

In the last twenty years, nonlocal peridynamics proposed by Silling [

This paper aims to develop a nonlocal peridynamic method for the evaluation of the metal ablation under high temperature. In the method, the peridynamic formulation for the heat conduction problem is obtained by Taylor’s expansion technique. To describe the moving boundary of the system caused by the thermal ablation, a simple and efficient moving boundary model in the peridynamic framework is proposed, in which the ablated states of the material points are represented by an additional scalar field. It is worth mentioning that due to the introduction of the scalar field, there is no need to update the computational domain and the horizon of material points during the whole computational process, which can reduce computational costs. Furthermore, a peridynamic contact algorithm is presented to determine the contact relationship between the ablated system and the heat carrier, which can be simply and conveniently achieved because of the automatic non-interpenetration properties of the peridynamic method. It is noted that during the calculation, all the material points, that is, the boundary material points (BMP), internal material points (IMP) and ablated material points (AMP), will change types due to the occurrence of the thermal ablation. In addition, the computational procedure of the present method is given out in detail and the effectiveness of the method is demonstrated by several representative numerical examples.

The remaining sections of this paper are organized as follows.

On the basis of the non-local peridynamic model and the corresponding spatial uniform discretization as shown in

In addition, based on Taylor’s expansion technique, the temperature

Substituting

Due to the symmetric property of the integral domain, e.g.,

It is noted that

Next, two kinds of weight functions are considered, i.e.,

Consequently, the peridynamic formulation of the one and two-dimensional transient heat conduction problems with the triangular weight function, for example, can be expressed as

In addition, both the Dirichlet (temperature) and Neumann (heat-flux) boundary conditions are considered in this paper. To impose these above boundary conditions, the fictitious material points are added outside the corresponding boundaries. For the Dirichlet boundary condition, the given temperature values are directly applied to the additional fictitious material points and remain constant all the time. For the Neumann boundary conditions, the given heat-flux values are indirectly imposed on the additional fictitious material points through the linear distributed temperatures as shown in

The thermal ablation is a common and direct way that may arise the serious failure for the metal structure under high temperature. The material is ablated while the temperature of the material reaches to its critical melting temperature of the material. Obviously, the geometry of the metal structure is changing along with the thermal ablation process. Therefore, to evaluate the thermal ablation process of the metal structure heated by a heat carrier with very high temperature, it is necessary to consider the moving boundaries besides the heat diffusion in the structure. For the finite element method, it is complex and uneconomical to deal with the problems with moving boundaries because the corresponding heat transfer matrix of the system needs to be reassembled when its geometry is changed during the numerical simulation. Fortunately, the peridynamics is a nonlocal method that expressed by an integral equation and the structure is discretized into many material points while a meshless method is adopted [

Taking the moving boundaries into account and substituting

It is emphasized that the seeking of the neighborhood for each material point only needs to be operated once at the initial time step due to the introducing of the scalar

In this paper, the thermal ablation process of the metal structure caused by a heat carrier with high temperature is evaluated. Except for the heat diffusion problem, the contact problem should also be considered in this simulation. Fortunately, the automatic non-interpenetration properties of the peridynamic method can naturally deal with the contact problem [

Consequently, the displacement increment

On the basis of the discretization in spatial and temporal, the discretized peridynamic formulation for the thermal ablation problem in metal under high temperature can be expressed as

In addition, the computational procedure of the proposed peridynamic method for the thermal ablation problem of the metal structures is listed in the following:

Set the control parameters (size of material points

Set the initial variables, such as the initial temperature

Loop for the time step (initialize

(3.1) Set

(3.2) Calculate the displacement increment

(3.3) Calculate the current temperature field on the basis of

(3.4) Update the ablated state scalar

(3.5) Update the classification of the material points, i.e., IMP, BMP and AMP.

If

Finish the computations and output the results.

In addition, the thermal conductivity between the metal structure and the heat carrier can be given by

In this section, several representative numerical examples are considered to evaluate the validity and accuracy of the proposed method. In addition, the relative errors of the temperature fields are defined as

Firstly, a simple transient heat conduction in a 2D plate is considered to investigate the validity and accuracy of the present method. As shown in

The initial and boundary conditions are as follows:

For the numerical simulation, three kinds of horizons of material points are taken into account, i.e.,

To investigate the validity and effectiveness of the present method for the evaluation of metal ablation under high temperature, an Al plate heated with a laser is considered. As shown in

Next, a rectangle Al plate ablated by a heat carrier is considered to examine the present contact algorithm. As shown in

Finally, the ablation process of the lower head of the RPV heated by core melt, which is simplified from the nuclear engineering problems, is investigated [_{2} and molten metal are

This paper presents a nonlocal peridynamic method for the evaluation of the thermal ablation in metal under high temperature. Firstly, the peridynamic formulation for the transient heat conduction problem is derived based on Taylor’s expansion technique. To simulate the thermal ablation problem, whose geometry is changed, a simple and efficient moving boundary model in the peridynamic framework is proposed by introducing a scalar field to describe the ablated states of material points. In addition, on the basis of the automatic non-interpenetration properties of the peridynamic method, an effective contact algorithm is suggested to determine the contact relationship between the ablated system and the additional heat carrier. Furthermore, the corresponding computational procedure is given out in detail. Finally, several representative numerical examples are taken into account. These results obtained by the present method fit well with the reference solutions, which demonstrates the validity and accuracy of the present method. Moreover, the present peridynamic method can be extended to analyze the coupling thermo-, deformation-, ablation- and fracture problems in the future.