Talat Lecture 3300: Fundamentals Of Metal Forming

TALAT Lecture 3300

Fundamentals of Metal Forming 18 pages, 27 figures Basic Level

prepared by Klaus Siegert and Eckart Dannenmann, Institut für Umformtechnik, Universität Stuttgart

Objectives: − a brief review of the fundamental terms and laws governing metal forming at room temperature as well as at high temperatures. This lecture is a necessary prerequisite to understand the more specific treatment of metal forming subjects such as forging, impact extrusion and sheet metal forming in the subsequent TALAT Lectures 3400 to 3800.

Prerequisites: − General background in production engineering, machine tools

Date of Issue: 1996  EAA - European Aluminium Association

3300

Fundamentals of Metal Forming

Table of Contents 3300 Fundamentals of Metal Forming ............................................................2 3301 Introduction................................................................................................... 3 3301.01 Definition of Forming ..............................................................................3 3302 Terms for Classifying Forming Processes .................................................. 4 3302.01 Classification by State of Stress (Figure 3302.01.01)..............................4 3302.02 Classification by Type of Raw Material (Figure 3302.02.01) .................4 3302.03 Classification by Forming Temperature...................................................5 3302.04 Classification by Methods of Induction of Forces into the Work-Piece..5 3303 Characteristic Values and Basic Laws of Metal Forming......................... 6 3303.01 Flow Stress...............................................................................................6 3303.02 Plastic Strain, Rate and Acceleration.......................................................7 Logarithmic (True) Plastic Strain....................................................................... 7 Logarithmic Strain in Upsetting ......................................................................... 7 Law of Volume Constancy .................................................................................. 8 Plastic Strain Rate .............................................................................................. 8 Plastic Strain Acceleration ................................................................................. 9 3303.03 Plastic Flow under Combined Stresses ....................................................9 Criteria for Plastic Flow..................................................................................... 9 Maximum Shear Stress Hypothesis................................................................... 10 Mises Flow Criterion ........................................................................................ 11 Yield Criteria for Plane Stress (Yield Locus) ................................................... 12 3303.04 Law of Plastic Flow ...............................................................................12 3303.05 Flow Curves .............................................................................................13 General Definition of the Flow Curve .............................................................. 13 Flow Curves at Room Temperature.................................................................. 13 Flow Curves at Elevated Temperatures............................................................ 14 3303.06 Average Flow Stress ..............................................................................16 3303.07 Energy Considerations ...........................................................................16 Forming Energy ................................................................................................ 16 Heat Development during Forming .................................................................. 17 Literature/References ............................................................................................. 18 List of Figures.......................................................................................................... 18

TALAT 3300

2

3301 Introduction

3301.01

Definition of Forming

The general description given in Figure 3301.01.01 defines metal forming by plastic deformation and distinguishes it from other forming and shaping processes like casting and machining.

Definition of Forming

Forming is a fabrication process for solid substances by controlled plastic deformation in order to obtain alterations of: - the form, - the material properties and/or - the surface properties, whereby the mass and material continuum remain unchanged.

K.Siegert alu Training in Aluminium Application Technologies

TALAT 3300

Definition of Forming

3

3301.01.01

3302 Terms for Classifying Forming Processes • • • •

Classification by State of Stress Classification by Type of Raw Material Classification by Forming Temperature Classification by Methods of Induction of Forces into the Work-Piece

3302.01

Classification by State of Stress (Figure 3302.01.01)

Terms for classifying the forming process:

Classification by State of Stress Pressure Forming

DIN 8583

Rolling, Open-Die Forming, Die Forming, Indenting, Pressing Through

Tension-Compression Forming

DIN 8584

Drawing, Deep Drawing, Collar Forming, Compressing, Upset Bulging

Tension Forming

DIN 8585

Stretch Reducing, Bulge Forming, Stretch Forming

Bend Forming

DIN 8586

Bending with Linear Tool Movement, Bending with Rotating Tool Movement

Shear Forming

DIN 8587

Shear Displacement, Twisting

alu

Classifying the Forming Process by State of Stress

3302.01.01

Training in Aluminium Application Technologies

3302.02

Classification by Type of Raw Material (Figure 3302.02.01)

Terms for classifying the forming process:

Type of Raw Material Sheet Forming The raw material consists of flat parts of constant thickness. The parts produced have a three-dimensional form with approximately constant wall thickness ( ≈ raw material thickness).

Bulk Forming Raw parts are three-dimensional. The parts produced are also three-dimensional but often have very different wall thicknesses and/ or cross-sections.

alu Training in Aluminium Application Technologies

TALAT 3300

Classifying the Forming Process by Types of Raw Materials

4

3302.02.01

3302.03

Classification by Forming Temperature (Figure 3302.03.01)

Terms for classifying the forming process:

Forming Temperature Cold Forming Process in which the work-piece is not heated before forming, but instead formed at room temperature. ϑ = ϑRoom (ca. 20° C )

Warm Forming Process in which the work-piece is heated to an elevated temperature higher than room temperature before forming. ϑ > ϑ Room (ca. 20° C ) Classifying the Forming Process by Forming Temperature

alu Training in Aluminium Application Technologies

3302.04

3302.03.01

Classification by Methods of Induction of Forces into the Work-Piece (Figure 3302.04.01)

Terms for classifying the forming process:

Methods of Applying Force Process with Indirect Force Application (Deep Drawing) FN

Process with Direct Force Application (Upsetting) F

FSt

Forming Zone Bending Zone Force Transmission Zone Force Induction Zone

F

K. Siegert alu Training in Aluminium Application Technologies

TALAT 3300

Classifying the Forming Process by Methods of Applying Force

5

3302.04.01

3303 Characteristic Values and Basic Laws of Metal Forming • • • • • • •

3303.01

Flow Stress Plastic Strain, Rate and Acceleration Plastic Flow under Combined Stresses Law of Plastic Flow Flow Curves Average Flow Stress Energy Considerations

Flow Stress (Figure 3303.01.01)

Characteristic Values, Basic Laws

Flow Stress

kf =

F A

By comparison (technical stress)

σ=

F A0

A0

l0

Flow stress (true stress)

F

Conversion: with one obtains

l

The flow stress (resistance to plastic deformation) of a material is the stress required to initiate or continue plastic deformation under uniaxial state of stress.

A

ε = (l − l0 ) / l0 k f = σ (ε l + 1)

F alu

Definition of Flow Stress

Training in Aluminium Application Technologies

TALAT 3300

6

3303.01.01

3303.02

Plastic Strain, Rate and Acceleration

Logarithmic (True) Plastic Strain (Figure 3303.02.01)

Logarithmic (True) Strain The logarithmic strain ϕ (true strain; degree of deformation) is a measure of the permanent (plastic) deformation

F

A0

dl l0

A l0

As opposed to this, elongation (relative deformation)

dε =

l

l0

dl l = ln l1 − ln l0 = ln 1 . l l0

l1

l1

ϕl = ∫

dl 2

dl logarithmic (or true) strain dϕ = l

A1

dl l − l l ε = ∫ = 1 0 = 1 − 1. l l0 l0 l0 0 Conversion: with

 l1    = (ε + 1)  l0 

one obtains

ϕ l = ln(ε + 1) alu

dl 2

l1

F

Logarithmic (True) Strain

3303.02.01

Training in Aluminium Application Technologies

Logarithmic Strain in Upsetting (Figure 3303.02.02)

Logarithmic Strain in Upsetting  h1    h0 

ϕ h = ln

b   b0 

ϕ b = ln 1 

h1

h0

Cuboid

b0

l0

l1 b1

l   l0 

ϕ l = ln 1 

r0 r1  h1    h0 

ϕ h = ln

h1

h0

Circular Cylinder

r   r0 

ϕ r = ln 1  = ϕ t

alu

Logarithmic Strain in Upsetting

Training in Aluminium Application Technologies

TALAT 3300

7

3303.02.02

Law of Volume Constancy (Figure 3303.02.03)

h1

h0

Law of Volume Constancy

l1

l0

b0

b1

Assuming that during forming the volume of a cuboid remains constant, the following equation is valid for a homogeneous compression: V = h1 ⋅ b1 ⋅ l1 = h 0 ⋅ b 0 ⋅ l 0

so that:

 h1   b1   l 1    ⋅  ⋅  = 1  h 0   b0   l 0 

Taking the logarithms h  b  l  ln 1  + ln 1  + ln 1  = 0 of both sides:  h0 

 b0 

 l0 

ϕh +ϕh +ϕh = 0

or: alu

or

∑ϕ = 0

Law of Volume Constancy

3303.02.03

Training in Aluminium Application Technologies

Plastic Strain Rate (Figure 3303.02.04)

Plastic Strain Rate (True strain rate) ·

The true strain rate or logarithmic strain rate ϕ is the derivative of the logarithmic strain (true strain) ϕ with time t:

ϕ!=

dϕ dt

From the law of volume constancy one obtains: .

.

.

ϕh + ϕb + ϕl = 0 .

Σϕ

= 0 ·

One has to differentiate between the strain rate ϕ and the tool speed vwz. For a homogeneous compression where h = instantaneous height of the material being compressed, the following relation is valid:

ϕ!=

alu Training in Aluminium Application Technologies

TALAT 3300

vwz h

Plastic Strain Rate (True Strain Rate)

8

3303.02.04

Plastic Strain Acceleration (Figure 3303.02.05)

Plastic Strain Acceleration ""

The plastic strain acceleration ϕ is the derivative of the plastic strain rate ϕ with time t: "

&= ϕ& alu

dϕ& dt

Forming Strain Acceleration

3303.02.05

Training in Aluminium Application Technologies

3303.03

Plastic Flow under Combined Stresses

Criteria for Plastic Flow (Figure 3303.03.01)

Criteria for Plastic Flow Criteria for plastic flow describe the requirements which must be fulfilled in order for plastic deformation to occur under a multiaxial state of stress. The requirements for flow are met when an equivalent stress, σv , derived from the multiaxial stress state, equals the flow stress kf:

σv = kf In the forming technology, two types of flow hypothesis are used to derive the comparative stress σv : -the shear stress hypothesis according to TRESCA -the forming energy hypothesis according to v. MISES

alu

Criteria for Plastic Flow

Training in Aluminium Application Technologies

TALAT 3300

9

3303.03.01

Maximum Shear Stress Hypothesis (Figure 3303.03.02, Figure 3303.03.03, Figure 3303.03.04)

Shear Stress Hypothesis (1) Flow occurs when the maximum shear stress τmax reaches a value characteristic for the material, the so-called shear yield stress k: τmax = k . Based on the stresses ( σ1 > σ2 > σ3 ) in the MOHR stress circle, the following equations can be derived: τ τmax =

τmax =

1 ( σ1 − σ3 ) = k 2

τmax (=k)

1 ( σmax − σmin ) = k 2

alu Training in Aluminium Application Technologies

σ3 = σmin

σ2

σ1 = σmax

σ

3303.03.02

Shear Stress Hypothesis (1)

Shear Stress Hypothesis (2) For a uniaxial state of tensile stress ( σ1 = σmax , σ2 = σ3 = σmin = 0 ), the following relationship is valid: τ

σmax - σmin = σ1 = 2k τmax= k

and ( definition of flow stress )

σ2 = σ3 = 0

σ1 = kf .

σ1

σ

Considering the flow conditions ( σv = kf ), one obtains: σv = kf = σmax - σmin. Thus, flow starts when the difference between the largest and smallest principal normal stresses equals the flow stress. alu

Shear Stress Hypothesis (2)

Training in Aluminium Application Technologies

TALAT 3300

10

3303.03.03

Shear Stress Hypothesis (3)

According to the shear stress theory, the comparative deformation strain is equal to the largest value of the logarithmic deformation strain:

ϕ g = ( ϕ 1 , ϕ 2 , ϕ 3 ) max . ϕg is the principal logarithmic (or true) strain.

alu

Shear Stress Hypothesis (3)

Training in Aluminium Application Technologies

3303.03.04

Mises Flow Criterion (Figure 3303.03.05)

Distortion Energy (von-Mises) Theory Flow sets in when the elastic distortion energy for changing the form exceeds a criterical value.

If σ1 > σ2 > σ3, then the comparative stress is given by

σ v = kf =

1 2 2 2 (σ 1 − σ 2 ) + (σ 2 − σ 3 ) + (σ 3 − σ 1 ) . 2

Using the average stress

σm =

1 (σ 1 + σ 2 + σ 3 ) 3

one obtains

σ v = kf =

3 2 (σ 1 − σ m )2 + (σ 2 − σ m )2 + (σ 3 − σ m ) . 2

Then, according to the distortion energy theory, the comparative deformation strain becomes

ϕv =

2 2 (ϕ 1 + ϕ 2 2 + ϕ 32 ). 3 alu

Training in Aluminium Application Technologies

TALAT 3300

Distortion Energy Hypothesis (v. Mises)

11

3303.03.05

Yield Criteria for Plane Stress (Yield Locus) (Figure 3303.03.06)

Yield Criteria for Plane Stress σ3

The comparision of yield criteria for a plane state of stresses (σ2 = 0) indicates the stress combinations σ1 , σ3 at which flow sets in.

σ2 = 0

kf −σ1

-kf

σ1

kf -kf

Distortion energy theory (v. Mises)

−σ3 Maximum shear stress theory (Tresca) alu Training in Aluminium Application Technologies

The curves depicting the yield criteria can thus be considered as an illustration of the flow theory in the σ1 , σ3 plane state of stresses. The two flow theories sometimes deliver somewhat different stress values for the start of flow. This difference is, however, small and does not exceed 15%.

Yield Criteria for Plane Stress

3303.03.06

3303.04 Law of Plastic Flow (Figure 3303.04.01)

Law of Plastic Flow The law of plastic flow describes the correlation between stress and the resulting deformation strain for the plastic state. Assuming that the ratios of the deformation strains among each other remain constant during the process, the correlation between the deformation strain ϕ and the principal stress σ which causes the deformation can be given by:

1 (σ 1 + σ 2 + σ 3 ) 3 ϕ 1 : ϕ 2 : ϕ 3 = (σ 1 − σ m ) : (σ 2 − σ m ) : (σ 3 − σ m )

σm =

Important consequences: The logarithmic deformation strain attains the value zero when the corresponding principal stress equals σm. alu

Law of Plastic Flow

Training in Aluminium Application Technologies

TALAT 3300

12

3303.04.01

3303.05 Flow Curves General Definition of the Flow Curve (Figure 3303.05.01)

Flow Curve The flow stress kf of a material depends on - the logarithmic principal deformation strain ϕg "

- the logarithmic principal deformation strain rate ϕg - the temperature ϑ and, during the high speed forming, also on ""

- the principal deformation strain acceleration ϕg "

""

kf = f(ϕg, ϕg, ϑ, (ϕg)).

i.e.

The flow curve is the illustration of the flow stress kf as a "

""

function of ϕg, ϕg, ϑ and ϕg.

alu

Flow Curve

3303.05.01

Training in Aluminium Application Technologies

Flow Curves at Room Temperature (Figure 3303.05.02, Figure 3303.05.03)

Flow Curves at Room Temperature (1) In the range of cold forming (forming temperature ϑ is considerably lower than the recrystallisation temperature ϑRekr ), the flow stress kf for most metallic materials depends only on the logarithmic principal deformation strain ϕg:

k f = f (ϕg )

kf

This dependence can be replaced for a number of materials by the approximate relationship

k f = a ·ϕ ng (valid for ϕg ≠ 0, i.e. for kf ≥ Rp0.2 respectively approximation for kf ≥ ReH) (a and n are material constants; n is called strain hardening exponent) alu

ϕg

Flow Curves at Room Temperature (1)

Training in Aluminium Application Technologies

TALAT 3300

k f = a ·ϕ ng

13

3303.05.02

Flow Curves at Room Temperature (2) By taking the logarithm of the equation kf = a·ϕgn

log k f = n log · ϕ g + log · a The illustration of a flow curve of the form kf = a· ϕgn in a coordinate system with axes in a logarithmic scale is a straight line whose gradient is the coefficient n.

log k f log k f = n log · ϕ g + log · a ∆ log k f

α ∆ log ϕ g

n = tan α =

∆ log k f ∆ log ϕ g

The coefficient n is a measure of the amount by which a material hardens with increasing deformation strain ϕg and is therefore known as the strain hardening coefficient. Typical values of n for an aluminium-killed steel are in the range of 0.2 ≤ n ≤ 0.25

log ϕ g

and for aluminium sheet alloys (AlMg0,4Si1,2 ka, AlMg,5Mn w) in the range of 0.2 ≤ n ≤ 0.3

alu Training in Aluminium Application Technologies

Flow Curves at Room Temperature (2)

3303.05.03

Flow Curves at Elevated Temperatures (Figure 3303.05.04, Figure 3303.05.05 and Figure 3303.05.06)

Flow Curves at Elevated Temperature (1)

Flow Stress kf

180 Material Al 99.5 N / mm² " -1 140 120

ϕg = 4 s

240°C

100 80 60

During forming at elevated temperatures (warm forming), the flow stress kf depends on the logarithmic principal deformation strain ϕg , the forming temperature ϑ and the logarithmic principal deformation strain rate " (deformation strain rate) ϕg:

360°C

"

kf = f(ϕg , ϑ , ϕg)

480°C

40 20 0

20°C 120°C

0.2 0.4 0.6 0.8 1.0 1.2

As a rule, the flow stress kf decreases with increasing temperature ϑ for a given logarithmic principal deformation strain ϕg,

Logarithmic Principal Deformation Strain ϕg Source: Bühler a.o alu Training in Aluminium Application Technologies

TALAT 3300

Flow Curves at Elevated Temperature (1)

14

3303.05.04

Flow Curves at Elevated Temperature (2)

Flow Stress kf

100 N / mm² 80

"

ϕg = 63 s "

60

ϕg = 4 s

20

- With increasing temperature ϑ , the influence of the logarithmic principal deformation strain ϕg on the flow stress kf decreases.

-1 "

- The influence of the deformation strain rate ϕg on the flow stress kf increases with increasing ϕg = 0.25 s temperature ϑ. For "a given logarithmic principal deformation strain ϕg and a given . forming temperature ϑ, the flow stress kf increases with Material Al 99.5 " increasing deformation strain rate . ϕg Temperature ϑ = 360°C "

40

-1

-1

0 0.2 0.4 0.6 0.8 1.0 1.2 Logarithmic Principal Deformation Strain ϕg

Source: Bühler a.o.

alu

Flow Curves at Elevated Temperature (2)

3303.05.05

Training in Aluminium Application Technologies

Flow Curves at Elevated Temperature (3)

Flow Stress kf

N / mm² 200

20°C 120°C 100 240°C 80 60 360°C 40 ϕg = 1 C 480° Material Al 99.5 20 40 s-1 63 0.25 Logarithmic Principal " Deformation Strain Rate ϕg

For a given logarithmic principal deformation " strain ϕg and a given forming temperature ϑ, the relationship between the flow stress kf and the deformation strain rate ϕg is given approximately by the equation m k f = b ⋅ ϕ! g

The exponent m is a measure of the hardening of the material which depends on the deformation strain rate. It increases with increasing temperature.

Source: Bühler a.o alu Training in Aluminium Application Technologies

TALAT 3300

Flow Curves at Elevated Temperature (3)

15

3303.05.06

3303.06 Average Flow Stress (Figure 3303.06.01)

Average Flow Stress The calculation of stresses, energies and forces is simplified, if one uses an equivalent constant flow stress instead of the actual flow stress kfm. For a forming process in the range 0 ≤ ϕg ≤ ϕg1 , it is defined as

kf kf (ϕg)

kf1 kfm kf0

ϕ g1

∫k ( ϕ f

0

g

k fm =

) dϕ

ϕg1

∫k ( ϕ f

g

0

) dϕ

kf 0 + kf 1 2

kf0 - flow stress at start of process (ϕg = 0) kf1 - flow stress at end of process (ϕg = ϕg1)

ϕg

alu

ϕ g1

ϕ g1

As an approximation, one can use

k fm = 0

1

Average Flow Stress

3303.06.01

Training in Aluminium Application Technologies

3303.07

Energy Considerations

Forming Energy (Figure 3303.07.01)

Forming Energy Total energy (effective forming energy)

Ideal forming energy The ideal forming energy W id is that part of mechanical energy which has to be used for the forming process without external friction and internal displacements.

The total forming energy Wges includes the ideal forming energy Wid as well as the energy required to overcome the external friction (WR) and the internal displacement (WSch), so that

The following relation is valid for the forming energy Wid:

Wges = Wid + WR + WSch

Wid = V ∫ k f ( ϕ g ) dϕ

where V is the formed volume. Using the average flow stress kfm, one obtains

Wid = V k fm ϕ g alu Training in Aluminium Application Technologies

TALAT 3300

Forming Energy

16

3303.07.01

Heat Development during Forming (Figure 3303.07.02)

Heat Developed during Forming Forming processes are irreversible processes. The major part of the energy applied for the forming process is converted into heat, causing the work-piece to warm up. Assuming that the total forming energy Wges is converted into heat and that no heat is lost to the environment (tool), the rise in temperature is given by the equation

∆ϑ =

Wges V * ρ * cp

(V formed volume, ρ density and cp specific heat of the work-piece material)

alu Training in Aluminium Application Technologies

TALAT 3300

Heat Developed during Forming

17

3303.07.02

Literature/References K. Lange (Editor): Umformtechnik, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1984

List of Figures

Figure No.

Figure Title (Overhead)

3301.01.01

Definition of Forming

3302.01.01 3302.02.01 3302.03.01 3302.04.01

Classifying the Forming Process by State of Stress Classifying the Forming Process by Types of Raw Materials Classifying the Forming Process by Forming Temperature Classifying the Forming Process by Methods of Applying Force

3303.01.01 3303.02.01 3303.02.02 3303.02.03 3303.02.04 3303.02.05 3303.03.01 3303.03.02 3303.03.03 3303.03.04 3303.03.05 3303.03.06 3303.04.01 3303.05.01 3303.05.02 3303.05.03 3303.05.04 3303.05.05 3303.05.06 3303.06.01 3303.07.01 3303.07.02

Characteristic Values, Basic Laws: Flow Stress Logarithmic (True) Strain Logarithmic Strain in Upsetting Law of Volume Constancy Plastic Strain Rate (True Strain Rate) Forming Strain Acceleration Criteria for Plastic Flow Shear Stress Hypothesis (1) Shear Stress Hypothesis (2) Shear Stress Hypothesis (3) Distortion Energy Hypothesis (v. Mises) Yield Criteria for Plane Stress Law of Plastic Flow Flow Curve Flow Curves at Room Temperature (1) Flow Curves at Room Temperature (2) Flow Curves at Elevated Temperature (1) Flow Curves at Elevated Temperature (2) Flow Curves at Elevated Temperature (3) Average Flow Stress Forming Energy Heat Developed during Forming

TALAT 3300

18