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European Journal of Applied Sciences – Vol. 11, No. 6

Publication Date: December 25, 2023

DOI:10.14738/aivp.116.16052

Yang, C. C., Nguyen, T. V., & Andres, J. C. (2023). The Cold Forming Analysis of Stainless Steel Socket-Head Screws. European

Journal of Applied Sciences, Vol - 11(6). 225-237.

Services for Science and Education – United Kingdom

The Cold Forming Analysis of Stainless Steel Socket-Head Screws

Chih-Cheng Yang

Department of Mechanical and Automation Engineering, Kao Yuan University,

Taiwan

Tu Van Nguyen

Graduate School of Metal Technology Industry, Kao Yuan University, Taiwan

Jhonel Cortez Andres

Graduate School of Mechatronic Science and Technology, Kao Yuan University,

Taiwan

ABSTRACT

A multi-stage cold forming process for the manufacture of Allen screws (I) and

hexalobular socket screws (II) is studied numerically with AISI 316 stainless steel.

The cold forming processes through three stages includes two upsetting

operations and backward extrusion over a moving punch. The numerical

simulations of cold forming are conducted using the finite element code of

DEFORM-3D. The formability of the workpiece is studied numerically, such as the

effect on forming load responses, maximum forming loads, effective stress and

effective strain distributions and metal flow pattern. In the three-stage forming

process, in the forming stages of two upsetting and one backward extrusion at the

upper face of the workpiece, the effective stresses in the head of the workpiece are

significantly high, and the effective strains are also significantly high due to large

deformation. The maximum effective stresses of 933 MPa for the last stage of

forming types (I) and (II) are the same. The effective strain responses for the last

stage of forming types (I) and (II) are very similar. The flow line distributions of

the last stages both for forming types (I) and (II) are also very similar, which are

more severely bent and highly compacted in the zone beneath the socket cavity

due to severe structure deformation. For the maximum axial forming load and

forming energy, the second stage of secondary upsetting to form a larger outer

diameter cylindrical head and simultaneously centering at the upper end is the

largest among the three stages. The total maximum axial forming loads from the

first to the last stages are 268.9kN for the three-stage forming of type (I) and

260.0kN for the three-stage forming of type (II); and the total forming energies are

about 587.0J for the type (I) forming and 564.5J for the type (II) forming.

Keywords: cold forming, socket-head screws, AISI 316 stainless steel, formability,

forming load.

1 INTRODUCTION

The cold forming process is widely applied in the manufacture of various component

products. Multi-stage cold forming is widely used in many industries, particularly in

manufacturing fasteners and special parts. High mechanical properties, good surface

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European Journal of Applied Sciences (EJAS) Vol. 11, Issue 6, December-2023

appearance and good accuracy are generally capable to be achieved without further process.

Multi-stage cold forming is a high-speed forming process in which the billet is formed

sequentially through multiple stations [1].

There are many studies on cold forming processes. There are also many cold forming studies

using numerical simulation to predict forming design and simulation parameter settings. Joun

et al. [2] presented a numerical simulation technique for the forging process with a spring- attached die. They applied a penalty rigid-viscoplastic finite element method together with an

iterative force-balancing method to investigate the significance of metal flow lines for quality

control and the effects of spring-attached dies on the metal flow lines and the decrease in

forming load. The application of a commercial general finite element software of ANSYS to

model a forming operation was presented by Roque and Button [3]. They developed models

to simulate the ring compression test and to simulate an upsetting operation which was one

stage of the automotive starter parts manufacturing process. MacCormack and Monaghan [4]

proposed a three-stage cold forging process to form the spline shape in the head of an

aerospace fastener. They gained insights into the operation through numerical analysis of

strain, damage, and flow patterns in all three stages.

To analyze the formability of the multi-stage forging process, Park et al. [5] applied the finite

element method to establish a systematic process analysis method for the multi-stage forming

of a constant velocity joint outer race. Farhoumand and Ebrahimi [6] used the FE code

ABAQUS on the analysis of the forward-backward-radial extrusion process to investigate the

influence of geometric parameters such as die corner radius and gap height and process

conditions such as friction on the process. The numerical results were compared with

experimental data in terms of forming loads and material flow in different regions. The

hardness distribution of the longitudinal section of the product was to verify the numerical

strain distribution. Ji et al. [7] presented the numerical code of DEFORM_2D to study the

forming mechanism of a five-stage cold extrusion process for shaft parts used in gearboxes.

They showed that the five-stage cold extrusion process is feasible and obtained the forming

rules. Paćko et al. [8] applied the finite element analysis to predict and optimize a bolt forming

process. They investigated bolt forming process consisted of six stages including cutting, three

upsetting stages, backward extrusion, and trimming. Several tool modifications were

proposed and analyzed using numerical simulation. Yang and Lin [9] presented the numerical

and experimental studies on two forming modes for two-step extrusion forming of AISI 1010

carbon steel. The numerical results were compared with experimental data in terms of

forming loads. The numerical results for the effective strain distributions are consistent with

the experimental hardness distribution. Winiarski and Gontarz [10] presented a new metal- forming process to produce two-step outer flanges on the hollow parts extruded by a movable

sleeve. They applied the new method to bring the end flange of the 6060-aluminum alloy

tubular billet. The cold-forming process was designed based on numerical simulations and

experiments. The experimental results verified the feasibility of cold forming a two-step

flange with a diameter approximately twice the outer diameter of the tubular blank. Obiko et

al. [11] conducted a three-dimensional finite element analysis using DEFORM 3D to

investigate the plastic deformation behavior during forging of X20CrMoV121 steel. The

influence of forging temperature on the strain, stress and particle flow velocity distribution

during the forging process was investigated. Francy et al. [12] dealt with input process

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Yang, C. C., Nguyen, T. V., & Andres, J. C. (2023). The Cold Forming Analysis of Stainless Steel Socket-Head Screws. European Journal of Applied

Sciences, Vol - 11(6). 225-237.

URL: http://dx.doi.org/10.14738/aivp.116.16052

parameter optimization in an extrusion process using DEFORM-3D software and Taguchi

approach. The numerical simulations were conducted by DFORM-3D used for expecting

minimum force attained in cold forward extrusion process.

Byun et al. [13] studied numerically on multi-stage cold forging of SUS304 ball studs. The

plastic deformation behavior of SUS304 from room temperature to 400°C was investigated

and a general method was used to express the flow stress as a close-form function of strain,

strain rate, and temperature. It is optimal at high strains, especially during multi-stage cold

forging. Petkar et al. [14] presented the use of a multi-layered feed forward artificial neural

network (ANN) model to determine the effects of process parameters such as billet size,

reduction ratio, punch angle, and land height on forming behavior, namely, effective stress,

strain, strain rate, and punch force in a cold backward extrusion forming for AISI 1010 steel.

FE simulation along with the developed artificial neural network model scheme could benefit

the cold forging industry in minimizing the process development effort in terms of cost and

time. Jo et al. [15] developed a multi-stage cold forging process using finite element analysis to

manufacture a high-strength one-body input shaft with a long body and no separate parts. A

proof-of-concept for the design and development of a multi-stage cold forging process was

provided to manufacture a one-body input shaft with improved mechanical properties and

material recovery. Lee et al. [16] proposed to use the multi-stage cold forming process to

reduce the solenoid valve manufacturing cost while satisfying dimensional accuracy and

performance. The forming process was divided into six stages to improve the dimensional

accuracy of the outer diameter, full length and slot part of the armature. Through the

proposed process design for the multi-stage cold forming process, the dimensional accuracy

of the test product was improved.

Szala et al. [17] investigated the hardness behavior and microstructure of 42CrMo4 steel

hollow parts with external flanges. Cold forming of metals led to the work-hardening of steels.

Metallographic studies verified that flow line arrangement was appropriate, which agreed

with the numerical results. The metal forming process did not influence the microstructural

uniformity of the flanged hollow parts. The final external flange part demonstrated a high

quality which was free of plastic deformation non-uniformity. Yang and Liu [18] presented a

numerical and experimental study on a five-stage cold forming process for manufacturing

AISI 1010 relief valve regulating nuts. The numerical simulation and experimental results

were in good agreement for the forming force growth tendency. The effective strain

distributions were consistent with the measured hardness distributions. Highly compacted

grain flow lines also resulted in higher hardness. Yang et al. [19] numerically studied a multi- stage cold forming process for the manufacture of AISI 1022 eccentric parts. The forming

processes through five stages and four stages include two-step forward extrusion, eccentric

upsetting, and backward extrusion over a moving punch. The formability of the workpiece is

studied numerically, such as the effect on forming force responses, maximum forming forces,

effective stress and strain distributions and metal flow pattern. Although the total maximum

axial forming forces of the four-stage forming are smaller than those of the five-stage forming,

the maximum lateral forming force in the last stage of the four-stage forming is almost five

times that of the last stage of the five-stage forming. Increasing lateral forging force may lead

to wear and damage of the punch. Tao et al. [20] aimed to determine an appropriate cold

forming process for thin-walled A286 superalloy tube with ideal forming quality. They