Understanding the deformation and fracture mechanisms in backward flow-forming process of Ti-6Al-4V alloy via a shear modified continuous damage model

https://doi.org/10.1016/j.jmatprotec.2021.117060Get rights and content

Highlights

  • Studied three different roller arrangements in backward flow-forming via user defined sub-routines in a FE framework.

  • Created 3D fracture strain maps for stress triaxiality/Lode parameter and stress triaxiality/thermal softening factor.

  • Highligted the limitations of the wedge flow-forming test to evaluate the flow-formability.

  • Characterized the fracture locus to evaluate the flow-formability.

  • Developed a summary chart correlating the process parameters and flow-formability.

Abstract

A shear modified coupled damage criterion based on continuum damage mechanics has been proposed in this study. Khan-Huang-Liang (KHL) model is implemented to predict the constitutive behavior of Ti-6Al-4 V (Ti64) alloy. A VUMAT subroutine has been developed for the damage model using a stress integration algorithm. Multiple simulations with tensile, compression and shear geometries are carried out in Abaqus/Explicit and compared with the experimental results to benchmark the hardening and damage criteria. The flow forming process involves a complex triaxial state of stress. This study is focused on understanding the contribution of triaxiality and shear during deformation and fracture in the flow-forming process with different roller arrangements. For this purpose, the flow-forming processes with three different roller arrangements, single roller, three roller, and wedge roller, are modeled, and their formability is compared by implementing a shear modified continuous damage model. A single roller flow-forming (SRF) arrangement undergoes high triaxiality due to excessive material displacement by the roller and high strain gradient in the axial direction. The fracture occurs near the interface of the reducing and thinning zone. The three-rollers flow-forming (TRF) provided maximum reduction till fracture and material fails due to excessive strain in the thinning zone at a relatively large percentage reduction. The wedge roller flow-forming (WRF) suffers a lack of uniform material softening, and fracture occurs near the interface of the uplift and reducing zone under high triaxiality. 3-D process maps have been developed for predicting fracture strain as a function of stress triaxiality/Lode parameter and stress triaxiality/thermal softening factor (E/σ¯2). Finally, a summary chart correlating the parameters, and flow-formability has been developed.

Introduction

The phenomenon of void nucleation, growth, and microcracks induced by large plastic deformations in metals is called ductile fracture. This phenomenon has been extensively studied by means of micro-mechanics analysis by pioneer authors like Freudenthal (1950); McClintock (1968), and subsequent studies. They presented criteria of limiting- threshold value of a variable/set of variables based on micro-mechanical analysis to predict the crack formation in the ductile materials. The criteria of limiting value of a variable/set of variables to predict ductile fracture can be referred as the ductile fracture criteria (DFCs). DFCs are mainly divided into two different categories of the modeling approach, i.e., uncoupled and coupled criteria. In the uncoupled damage modeling approach, the damage evolution is not associated with the yield surface of the material, and it does not affect the state of stress and strain during deformation. The damage in these criteria is generally characterized by a critical value of the parameter, such as strain energy, strain, stress triaxiality, etc. Freudenthal (1950) presented the criteria based on the critical value of plastic work in the material. Cockroft and Latham (1968) proposed an empirical model with underlying non dimensional stress concentration factor (σ1/σ¯) effect. Rice and Tracey (1969) introduced the effect of multiaxial stress state and suggested that void growth rate amplifies by an exponential function of the mean normal stress under moderate and high triaxiality conditions. Ayada et al. (1984) proposed a relatively simple relation considering the effect of stress triaxiality (σm/σ¯) on void growth while neglecting the nucleation and coalescence effect. Another important development was proposed by Johnson and Cook (1985), who introduced a multiplicative model, including the effect of stress triaxiality, strain rate, and temperature on fracture strain. The Johnson-Cook damage model was popularly implemented in various processes with varying strain rates and temperature conditions. In another breakthrough development, Bai and Wierzbicki (2008) suggested that fracture occurs distinctly under different mode of deformation and introduced the effect of hydrostatic pressure and Lode angle (θ) on damage behavior of the material. They postulated a fracture locus in the space of stress triaxiality, Lode parameter, and equivalent fracture strain. The coupled criteria considered the effect of stress and strain on damage evolution. In the coupled damage criteria, the constitutive equations incorporate a damage factor. Therefore, the yield surface during plastic deformation accounted for damage evolution. The coupled damage models are challenging to implement in finite element (FE) code as compared to the uncoupled models. Gurson (1977) proposed a metal porosity based coupled damage model, which was further modified by the Tvergaard and Needleman (1984) and popularly known as Gurson–Tvergaard–Needleman (GTN) model. The GTN micromechanics based model formulates the pressure-sensitive plastic flow along with the presence of initial void volume fraction as imperfection. The interaction with other state variables during plastic deformation leads to an increase in void volume density, and fracture occurs at a critical value. The damage evolution in the GTN model is divided into three stages during deformation, the damage starts with voids nucleation, followed by void growth, and ultimately failure occurs due to void coalescence. Another widespread coupled criterion was presented by Lemaitre (1985a,1985b). This model is based on continuum damage mechanics and popularly known as the Lemaitre model. The proposed continuous damage model (CDM) incorporated a damage variable (D) to capture the damage progression and material degradation. According to the CDM, the micro-cracks initiate in the material at a critical value of the damage variable (D). The advantage of the CDM criterion is that it requires comparatively fewer material parameters than GTN model and is rather easy to implement in an FE code.

The flow forming or tube spinning process is a method of forming high strength and thin precision tubes, where a preform tube is placed into a mandrel, and its thickness reduction with the help of rotating rollers. The incremental nature of the flow forming process produces highly localized deformation; hence, the material undergoes high strain. The material flow instability (diametral growth, bulges, waviness, etc.) and ductile fracture are the common modes of failure in flow-forming process. The initial studies on the failure modes in flow-forming process were primarily focused on material flow instability. Kemin et al. (1997) carried out an elastoplastic finite element analysis to predict the diametral growth in the flowformed tube. The diametral growth increases with an increase in the thickness reduction while the feed rate has an appreciable effect on the diametral growth. Jahazi and Ebrahimi (2000) studied the effect of flow-forming parameters on the surface defects like waviness and microcracks. They found that the surface defects could be characterized by the ratio of the contact length in hoop direction (S) to the contact length in the axial direction (L). The S/L ratio mainly depends on the attack angle, and the reduction ratio and a higher S/L ratio can minimize the defects in the material. The uncoupled damage criteria are popularly used to predict the fracture in metal spinning and tube flow-forming process due to its simplicity in implementation. Huang et al. (2008) implemented a shear failure model to predict the fracture in the radial direction during the single roller splitting spinning process. However, the study was mainly confined to the analysis of the spinning force and stress distribution with limited focus on crack prediction. Ma et al. (2015) implemented several uncoupled DFCs in Abaqus® to predict the spinnability of TA2 titanium alloy. Based on their results, they concluded that the Cockcroft–Latham (C–L) model predicted the failure in the flow-formed components most accurately. Zhan et al. (2009) compared C–L criterion and the Lemaitre model during the splitting spinning process. The Lemaitre model provided better accuracy in predicting the location and distribution of damage during the process. In a recent work, Wu et al. (2019) implemented a shear modified GTN model to predict the damage in the tube spinning process and concluded that the shear modified GTN model accurately predicts damage evolution and crack location in the spinning process. However, the disadvantage of the GTN model is that the implementation of the thermal softening effect in the constitutive equation is challenging.

The continuous damage model (CDM) has been implemented for some forming processes to predict the progress and the location of fracture. However to the best of authors’ knowldge, no study has been reported in the literature which utilizes the CDM model to predict fracture in the flow-formed components. In this work, a shear modified continuous damage model is proposed and implemented in a commercial Finite Element code and benchmarked for different loading conditions prior to predicting fracture in the flow-formed tube. The parameters for the material model have been estimated by conducting tests at a wide range of strain rates and temperatures on Gleeble® 3800 thermomechanical simulator. The purpose of this study is to understand the role of triaxial stress, shear, and thermal softening factor in deformation and fracture of the flowformed tube by implementing strain rate and temperature-sensitive constitutive equation and CDM model into an FE code. Different flow-forming roller arrangements and reduction angles are employed to vary the stress state, and the characterization is done using triaxiality-Lode angle parameter plots. This paper explicitly highlights the limitations of wedge flow-forming test and multiple single pass flow-forming tests with increasing reduction for evaluating the flow-formability of Ti64 tubes. The fracture locus has been characterized to evaluate the flow formability and process variables have been correlated qualitatively with flow formability.

Section snippets

Process description

A fully coupled thermomechanical finite element model of flow-forming process has been developed with three different roller arrangements viz. three rollers staggered flow-forming (TRF), single roller flow-forming (SRF), and wedge roller flow-forming (WRF) process. Figs. 1 (a)-(c) shows the three-dimensional depiction of TRF, SRF, and WRF arrangements, respectively. The setup of TRF comprises a mandrel, preform, and three rolls. Fig. 1 (a) shows the three roller setup arrangement, where rolls

Effect of roller arrangement

The damage evolution during the flow-forming of Ti alloy is affected by multiple factors. Eq. (13) shows the damage parameter as a function of equivalent stress, plastic strain, triaxiality, and lode parameter. Moreover, the equivalent stress depends on strain-rate and temperature. These parameters also affect the damage behavior of the material. The analysis is done to compare the evolution of various internal variables and their effect on deformation and damage behavior in SRF, TRF, and WRF

Limitations of wedge flow-formability test for Ti alloy

The wedge roller flow-formability test is popularly adopted to determine the maximum reduction in single pass during the flow-forming process. However, the maximum formability predicted by CDM based model is 21 %, which is much lower than the 40 % successful reduction using single roller and 50 % reduction in experimental work utilizing three rollers. (Depriester and Massoni (2013)) have achieved maximum of 64 % reduction in single pass of cold flowformed Ti64 tube with three rollers staggered

Conclusions

A shear modified continuous damage model (CDM) is proposed. The successful implementation and verification of the VUMAT based CDM model are done by performing various experiments with different geometry. The deformation behavior and fracture mechanism during SRF, TRF, and WRF processes are characterized. The formability and fracture zone is discussed by introducing the triaxiality vs. Lode angle parameter plot. The following conclusions can be drawn from this study:

  • The KHL model provides a

CRediT authorship contribution statement

Abhishek Kumar Singh: Methodology, Software, Formal analysis, Validation, Writing - original draft. Abhishek Kumar: Data curation. K. Narasimhan: Supervision, Writing - review & editing. Ramesh Singh: Conceptualization, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

Authors gratefully acknowledge the support of Center of Excellence in Steel Technology (COEST) for the use of Gleeble 3800 Thermomechanical Simulator.

References (30)

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