Autofrettage of layered and functionally graded metal–ceramic composite vessels

Abstract

The residual compressive stresses induced by the autofrettage process in a metal vessel are limited by metal plasticity. Here we showed that the autofrettage of layered metal–ceramic composite vessels leads to considerably higher residual compressive stresses compared to the counterpart metal vessel. To calculate the residual stresses in a composite vessel, an extension of the Variable Material Properties (X-VMP) method for materials with varying elastic and plastic properties was employed. We also investigated the autofrettage of composite vessels made of functionally graded material (FGM). The significant advantage of this configuration is in avoiding the negative effects of abrupt changes in material properties in a layered vessel – and thus, inherently, in the stress and strain distributions induced by the autofrettage process. A parametric study was carried out to obtain near-optimized distribution of ceramic particles through the vessel thickness that results in maximum residual stresses in an autofrettaged functionally graded composite vessel. Selected finite element results were also presented to establish the validity of the X-VMP method.

Introduction

Autofrettage is a process in which compressive residual stresses are induced in a vessel by applying and removing an internal pressure that is well beyond the vessel normal service pressure [1], [2], [3], [4], [5]. During the loading phase, a significant part of the vessel cross section undergoes plastic deformation and the unloading results in development of compressive residual stresses at the inner part and tensile residual stresses at the outer part of the vessel. The induced compressive residual stress at the inner vessel part leads to enhancement of vessel’s fatigue life and load-carrying capacity [6], [7], [8], [9], and thus longer service life under cyclic internal pressure. For metal vessels, the magnitude of the residual compressive stress that can be induced by the autofrettage process is limited by the plasticity of metal [10]. To put this in perspective, in Fig. 1, Fig. 2, we studied the residual stresses in a thick metal vessel induced by the autofrettage process. The results were calculated using the Variable Material Properties (VMP) method developed by Jahed and Dubey [11]. In this method, the linear elastic solution of a boundary value problem is used as a basis to generate its inelastic solution. The material parameters are considered as field variables and stress distributions are obtained as a part of solution in an iterative manner. In this analysis, the vessel was divided into thin strips (i.e. cylindrical elements) over its thickness and the VMP method was used to estimate the state of stress in the vessel. We assumed that the metal has bilinear elastic–plastic response under uniaxial loading with isotropic hardening behavior during unloading. The metal has elastic modulus, E_m = 56 GPa, tangent modulus, H_m = 12 GPa, and yield stress under uniaxial loading, ${\sigma }_y^m$ = 106 MPa – see Fig. 1A. The metal Poisson ratio, denoted by ${\nu }_m$, was assumed to be equal to 0.25. The thickness and internal radius of the vessel are denoted by t and R, respectively. Fig. 1B and C shows the residual hoop and radial stresses for a vessel with t/R = 1, respectively, subjected to different autofrettage pressures denoted by P. For low values of autofrettage pressure, the vessel behaves elastically over most of its sectional area during the loading phase of the autofrettage process (i.e. applying the internal pressure) and thus, the residual hoop stresses are considerable only close to the inner surface (bore) of the vessel (e.g. see the results for P = 50 MPa in Fig. 1B). In this case, the maximum residual hoop stress is generally lower than the metal yield stress. By increasing the autofrettage pressure, plastic deformation occurs over a larger sectional area of the metal vessel during the loading phase. For P = 100 MPa, the results show that the outer part of the metal vessel, x/R > 0.8, deforms only elastically during the loading phase of the autofrettage pressure, which manifests by a sudden change in the slope of residual stress curve at x/R ≅ 0.8. For P = 300 MPa, the metal vessel deforms plastically over its entire cross section during the loading phase. Note that there is very little difference between the calculated residual hoop stresses in the inner part of the metal vessel for P = 100 MPa and 300 MPa. The residual radial stresses are compressive through the thickness of the vessel with values that are generally much lower than the residual hoop stresses as quantified in Fig. 1C.

Fig. 2A summarizes the results of a parametric study on the induced residual hoop stresses at the inner surface of the vessel with different thickness to radius ratio. The residual hoop stress approaches zero for thin-walled vessels (i.e. small values of t/R) due to the quasi-uniform distribution of the stresses through the vessel thickness during the loading and unloading phases. For thicker vessels, the value of the residual stresses reaches its maximum at a critical t/R for each autofrettage pressure, which approximately corresponds to the thickness at which the autofrettage percent is 100% (i.e. the vessel deforms plastically over its entire cross-section area during the loading phase). For vessels thinner than the critical thickness, the residual stress at the inner surface remains constant by increasing the applied autofrettage pressure. For autofrettaged vessels with low values of autofrettage pressure (e.g. P = 50 MPa in Fig. 2A), there is also a maximum thickness at which the residual hoop stress in the vessel is non-zero since plastic deformation does not occur in thicker vessels during the loading phase. At a higher autofrettage pressure, a part of the vessel always undergoes plastic deformation during the loading phase, leading to non-zero residual stresses after unloading. The residual stress at the inner surface of the vessel, first increases by increasing the vessel thickness till the thickness reaches the critical thickness value discussed above and then decreases by increasing the vessel thickness, approaching zero as t/R → ∞. A complementary set of calculations was carried out to study the role of metal hardening characteristics on the induced residual stresses in an autofrettaged metal vessel. The results of this study are summarized in Fig. 2B, which shows that the maximum inducible residual stress is remarkably decreased and is achievable at a higher autofrettage pressure as the metal tangent modulus increases.

The above discussion clearly highlights a key limitation of autofrettaged metal vessels, which is its constriction by metal plasticity behavior. Several techniques have been proposed to address this limitation. Mughrabi et al. [12] and Feng et al. [13] proposed low-temperature autofrettage of vessels and showed that higher compressive hoop residual stress can be achieved by this technique. The key reason is that the stiffness and yield strength of metal are higher at low temperature and the thermal strains accumulated during warm up to room temperature elevates the compressive stresses induced in the vessel. Combination of autofrettage and shrink fit [14], [15], [16] and re-autofrettage [17], [18] have been also used to enhance the performance of vessels.

In this paper, we explore an alternative approach from the materials perspective. We considered two different vessels made of layered and functionally graded composites and studied the residual stresses in these vessels by the autofrettage process using a numerical method that is an extension of the Variable Material Properties (X-VMP). The developed method, which is introduced in our previous paper [19] and discussed in details in Section 2, allows us to analyze axisymmetric structures made of materials with varying elastic and plastic properties with high fidelity and efficiency. Our work complements the previous studies on axisymmetric functionally graded structures, including rotating disks with variable thickness [20], hollow cylinders subjected to internal pressure and/or tangential tractions on the outer surface [21], brake disks [22], and pressurized disks and cylinders [23].

Throughout this paper, the results based on finite element analysis are also provided to establish the validity of the X-VMP method using commercially available software, ABAQUS. The results for the autofrettage of metal–ceramic layered composite vessels, including bilayer and multi-layered vessels are presented in Section 3. In Section 4, the autofrettage of functionally graded ceramic-reinforced composite vessels is investigated and a parametric study is performed to obtain the near-optimized distribution of ceramic particles, which results in a maximum residual stress at the inner surface of the vessel. Conclusions are drawn in Section 5.