Loading conditions constrained wrinkling behaviors of thin-walled sheet/tube parts during metal forming

Highlights

• Initial geometric imperfections (GI) make the wrinkling prediction more sensitive.

• The wrinkling is more prone to occur under tension-compression stress state.

• Increasing normal constraints can effectively reduce wrinkling instability.

• Different loading conditions cause the inconsistent effects of the material role on wrinkling.

Abstract

With the increasing usages of high strength and lightweight materials, how to accurately predict and fully understand the wrinkling instability of thin-walled parts forming under various loading conditions, viz. stress states and normal constraints, is still a challenge for free-defect design and manufacturing. In this study, taking tension-compression stress state w/wo normal constraints (Yoshida test and deep drawing of sheets) and compression stress state w/wo normal constraints (axial compression and rotary draw bending of tubes) as the comparative cases, two kinds of geometric imperfections (GI), viz., random thickness imperfection (RTI) and geometric deflection imperfection (GDI) are introuduced and implemented into dynamic explicit finite element (FE) models to realize more sensitive prediction of the wrinkling instability. And then, a systematic comparative study on the critical wrinkling behavior and final wrinkling morphology under varous loading conditions has been studied. It is found that the wrinkling is more prone to occur under tension-compression stress state, and the wrinkling of the processes without normal constraint are severer than those with normal constraints. Furthermore, the effects of material parameters on the wrinkling are inconsistent in different processes, the reason proved to be the different loading conditions. When the degree of normal constraint increases, the influence of material properties becomes negligible. Combining the geometric and material parameters, the key issues affecting the wrinkling of thin-walled parts from the perspective of loading condition have been expounded, laying the foundation and theoretical guidance for the study of wrinkling behavior under different mechanical states.

Introduction

Due to the advantages of lightweight and high performance, thin-walled parts have been widely applied in many high-end equipment manufacturing fields such as aviation, aerospace and automobile (Cao and Banu, 2020). However, the wrinkling instability may easily occur in forming manufacturing of the thin-walled components, leading to poor performance of forming processes. It is known that the initiation and growth of wrinkles are significantly and interactively affected by multiple factors including geometric parameters, material properties and boundary conditions (João and Gérard, 2002). With the increasing usages of high strength and lightweight materials, complex loading conditions including stress states and normal constraints could be designed to break forming limit and improve the formability of difficult-to-form materials and structures (Yang et al., 2020). How to fully understand and accurately predict the wrinkling instability of thin-walled parts during metal forming process under various loading conditions is still a fundamental issue and all along a challenge for free-defect design and manufacturing (Li and Fu, 2019).

Over the years, great efforts have been conducted to investigate wrinkling behaviors of thin-walled parts in metal forming processes by using experimental, analytical and numerical methods (Liu et al., 2016). Various kinds of prediction methods such as minimum energy criterion based analytical method and FE based numerical method have been established to predict the wrinkling initiation and propagation in forming processes (Chen et al., 2021).

As for material properties, series of studies have been conducted to explore the relationship between material properties and the wrinkling risk. For deep drawing process, Saxena and Dixit (2010) studied on the flange wrinkling in square and circular cup drawing and found that the effects of hardening exponent n and initial yield stress σ_y on the wrinkling are additive in square cup but opposite in circular cup. The reason for these differences is attributed to the difference in the flange geometry and the essential reason of the wrinkling onset depends on the stress state in the flange. For tube axial compression process, Paquette and Kyriakides (2006) found that the wrinkling instability was strongly influenced by the hardening of the material, as higher hardening effectively delays the generation of the wrinkling, but when it comes to consider internal pressure, the effect of material property is relatively secondary. It is noted that effects of material properties on wrinkling are different or weakened when the same process comes to different stress states. Furthermore, the effects and significance of the same material property on wrinkling instability are even inconsistent for various forming processes. Taking the hardening exponent n and anisotropy parameter r for examples, Loganathan and Narayanasamy (2006) indicated that high normalized hardening and high anisotropy of material showed better resistance against the wrinkling in aluminum sheet drawing. Kim et al. (2010) found the same effects of these two material parameters on the wrinkling in cylindrical cup deep drawing process. However, Li et al. (2000) found that a higher r value promoted the growth of buckles in sheet tension test. Cao and Wang (2000) observed that the critical stress decreases gradually and monotonically with increasing r for plate wrinkling under tri-axial loading. Narayanasamy and Sowerby (1994) obtained that a higher r and a lower n could increase the wrinkling tendency in sheet drawing through a conical die. Wang and Cao (2000) explored that as n increased, the normalized critical stress was dramatically lowered, but the material anisotropy had almost indistinguishable effects on the wrinkling. However, there is not a comprehensive study on the inconsistent effects of material properties on wrinkling in different forming processes. The reason for the inconsistency may be the diverse stress states and normal constraints in the different processes. While the above assumption needs theoretical support.

As for geometric factors, some attempts have been carried out to study the effects of geometric parameters on the wrinkling instability in plastic forming processes. Neale and Tuǧcu (1990) investigated the influence of geometry parameters on the critical stress state in Yoshida test of sheets, and indicated that the critical stress for the onset of the wrinkling was significantly dependent on sheet thickness t and sheet partial curvature radius R. On this basis, Kim and Son (2000) found that the wrinkling tendency decreased as the sheet thickness decreased, and the ratio of R and t affected the deformation of the shell element, and the critical wrinkling stress decreased as the R increased. Haley and Kyriakides (2020) studied the wrinkling behavior dependent on the ratios of tube diameter and thickness (D/t) in tube axially crush deformation, and observed that increasing of the value of D/t would result in the growth of wrinkling degree. Tian et al. (2013) focused on the effects of geometric parameters on the wrinkling of thin-walled rectangular aluminum alloy wave-guide tubes in rotary-draw bending, and found that the ratio of width to height (b/h) and relative bending radius (R/h) greatly influenced the wrinkling behaviors. It can be summarized that consistent conclusions are obtained regarding effects of geometric parameters of thin-walled parts on the wrinkling instability.

As the above mentioned, besides the material properties and geometric parameters, another key influential factor of the wrinkling behavior of thin-walled parts in metal forming is the loading condition, viz. stress state and normal constraint, etc. Cao and Boyce (1997) examined the wrinkling behaviors of the sheet tension and drawing processes under normal constraints, and found that the wrinkling instability of sheets subjected to normal constraints was reduced effectively. Cao et al. (2007) conducted an innovative buckling test, “Contact Buckling Test”, and observed the same phenomenon that the die contact delayed the wrinkling initiation for both aluminum and steel sheets. However, they only put forward the sheet sample under one certain stress state. Yan (2016) established a wrinkling model of shear enforced thin-walled tubes under multiple die constraints, and found that the constraints in tube bending had a remarkable effect on decreasing the wrinkling degree, but he didn’t illustrate the effect of the constraint from a theoretical perspective and the relationship of the stress state and other influence factors. Du et al. (2020) investigated the morphology and characteristics of the critical wrinkling limit diagram (WLD) associated with nonuniform diagonal tensile test of sheets, and the results showed that the constraints do affect the critical wrinkling behavior. Morovvati et al. (2010) investigated wrinkling of two-layer (aluminum-stainless steel) sheets in the deep drawing process, and found that wrinkling could always be eliminated with an increase in the blank holder force (BHF). From above studies, it can be concluded that wrinkling tends to decrease when with constraints, while there is no deep exploration on how the stress state and normal constraint affecting wrinkling behavior in thin-walled sheet/tube forming.

As for prediction models, it is noted that the wrinkling initiation of thin-walled components are more sensitive to the initial geometric imperfections (GI) including random thickness imperfection (RTI) and geometric deflection imperfection (GDI). For instance, when the thickness of sheet metal is a little lower or higher than the design value, which is unavoidable in the manufacturing process of thin-walled parts, the stress distribution will be uneven, resulting in the unpredictable wrinkling. Therefore, when predicting the wrinkling behavior of the thin-walled parts in forming process, it is necessary to consider the effects of GI to make the prediction result more sensitive and more accurate (Rzeszut and Garstecki, 2009). Yan et al. (2020) presented a study on the buckling of spherical shells containing a thickness deflection, and obtained that thickness deflection greatly influenced the wrinkling behaviors. Li et al. (2019) implanted geometric micro-imperfections (GMI) into wrinkling prediction modeling for tube bending and axial compression and explored that the model implanting GMI can provide more sensitive wrinkling prediction than the normal model. Luo et al. (2019) modelled initial geometrical imperfections which was verified to be a reasonable method to describe the random field uncertainties with limited samples. Szymczak and Kujawa (2017) devoted to the effect of GI on the critical buckling load of thin-walled I-column axially compression, and the non-linear differential equations of the critical buckling loads were obtained. Papadopoulos and Papadrakakis (2005) investigated the effect of material and thickness imperfections on the buckling load of the cylinder axially compression based on the concept of an initial ‘imperfect’ structure, and observed that the prediction values combined GI were closer to the experimental results. However, GI including different forms are not subdivided clearly. Moreover, there are few reports on prediction model considering two or more GIs at the same time to make the model more sensitive to the wrinkling behaviors.

From the above, most studies focus on the wrinkling phenomena in one certain forming process for certain material type and geometric shape. The behaviors of the wrinkling instability in forming processes under different loading conditions of thin-walled sheet/tube still cannot be sensitively predicted or deeply revealed. So in this study, tension-compression stress state w/wo normal constraints (Yoshida test and deep drawing of sheets) and compression stress state w/wo normal constraints (axial compression and rotary draw bending of tubes) have been taken as the comparative cases. First, to realize more sensitive prediction of the wrinkling instability in various forming processes with different loading conditions, two different kinds of GIs are introduced and implemented into the prediction models. Then, a systematic comparative study on wrinkling behaviors under various loading conditions are analyzed.