TALAT Lecture 3300: Fundamentals of Metal Forming
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TALAT Lecture 3300: Fundamentals of Metal Forming

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This lecture gives 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 ...

This lecture gives 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 This lectures 3400 to 3800. General background in production engineering, machine tools is assumed.

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TALAT Lecture 3300: Fundamentals of Metal Forming TALAT Lecture 3300: Fundamentals of Metal Forming Document Transcript

  • 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 Definition of Forming 3301.01.01 TALAT 3300 3
  • 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 Rolling, Open-Die Forming, Pressure Forming DIN 8583 Die Forming, Indenting, Pressing Through Tension-Compression Drawing, Deep Drawing, Forming DIN 8584 Collar Forming, Compressing, Upset Bulging Tension Forming DIN 8585 Stretch Reducing, Bulge Forming, Stretch Forming Bending with Linear Tool Movement, Bend Forming DIN 8586 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 Classifying the Forming Process by 3302.02.01 Training in Aluminium Application Technologies Types of Raw Materials TALAT 3300 4
  • 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 ) alu Classifying the Forming Process by Training in Aluminium Application Technologies Forming Temperature 3302.03.01 3302.04 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 Process with Direct Force Application (Deep Drawing) (Upsetting) F FN FSt Forming Zone Bending Zone Force Transmission Zone Force Induction Zone K. Siegert F alu Classifying the Forming Process by Training in Aluminium Application Technologies Methods of Applying Force 3302.04.01 TALAT 3300 5
  • 3303 Characteristic Values and Basic Laws of Metal Forming • Flow Stress • Plastic Strain, Rate and Acceleration • Plastic Flow under Combined Stresses • Law of Plastic Flow • Flow Curves • Average Flow Stress • Energy Considerations 3303.01 Flow Stress (Figure 3303.01.01) Characteristic Values, Basic Laws Flow Stress F A 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. A0 F Flow stress kf = (true stress) A l0 By comparison F l σ= (technical stress) A0 Conversion: ε = (l − l0 ) / l0 with one obtains k f = σ (ε l + 1) F alu Definition of Flow Stress 3303.01.01 Training in Aluminium Application Technologies TALAT 3300 6
  • 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 dl logarithmic (or true) strain dϕ = dl 2 l l1 dl l ϕl = ∫ = ln l1 − ln l0 = ln 1 . l0 l l0 A0 dl As opposed to this, elongation dε = A l0 (relative deformation) l1 l0 l A1 dl l − l l l1 ε = ∫ = 1 0 = 1 − 1. l l0 0 l0 l0 Conversion:  l1  with   = (ε + 1)  l0  dl 2 F one obtains ϕ l = ln(ε + 1) alu Training in Aluminium Application Technologies Logarithmic (True) Strain 3303.02.01 Logarithmic Strain in Upsetting (Figure 3303.02.02) Logarithmic Strain in Upsetting  h1  ϕ h = ln   h0  Cuboid b  ϕ b = ln 1  h0 h1  b0  l  b0 l0 l1 ϕ l = ln 1  b1  l0  r0 r1  h1  Circular ϕ h = ln  h0  h0  h1 Cylinder r  ϕ r = ln 1  = ϕ t  r0  alu Logarithmic Strain in Upsetting 3303.02.02 Training in Aluminium Application Technologies TALAT 3300 7
  • Law of Volume Constancy (Figure 3303.02.03) Law of Volume Constancy h0 h1 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  of both sides: ln 1  + ln 1  + ln 1  = 0  h0   b0   l0  or: ϕh +ϕh +ϕh = 0 or ∑ϕ = 0 alu Training in Aluminium Application Technologies Law of Volume Constancy 3303.02.03 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: dϕ ϕ= ! 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: vwz ϕ= ! h alu Training in Aluminium Application Technologies Plastic Strain Rate (True Strain Rate) 3303.02.04 TALAT 3300 8
  • 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: & dϕ & & ϕ= dt alu Training in Aluminium Application Technologies Forming Strain Acceleration 3303.02.05 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 3303.03.01 Training in Aluminium Application Technologies TALAT 3300 9
  • 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 1 τmax τmax = ( σ1 − σ3 ) = k 2 (=k) σ2 σ σ3 σ1 = σmax 1 ( σmax − σmin ) = k = σmin τmax = 2 alu Shear Stress Hypothesis (1) 3303.03.02 Training in Aluminium Application Technologies 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 and ( definition of flow stress ) τmax= k σ2 = σ3 = 0 σ1 σ σ1 = kf . 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) 3303.03.03 Training in Aluminium Application Technologies TALAT 3300 10
  • 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 Training in Aluminium Application Technologies Shear Stress Hypothesis (3) 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 1 σ v = kf = (σ 1 − σ 2 ) + (σ 2 − σ 3 ) + (σ 3 − σ 1 ) . 2 2 2 2 Using the average stress 1 σm = (σ 1 + σ 2 + σ 3 ) 3 one obtains 3 σ v = kf = (σ 1 − σ m )2 + (σ 2 − σ m )2 + (σ 3 − σ m ) . 2 2 Then, according to the distortion energy theory, the comparative deformation strain becomes ϕv = 3 (ϕ 1 + ϕ 2 2 + ϕ 32 ). 2 2 alu Training in Aluminium Application Technologies Distortion Energy Hypothesis (v. Mises) 3303.03.05 TALAT 3300 11
  • Yield Criteria for Plane Stress (Yield Locus) (Figure 3303.03.06) Yield Criteria for Plane Stress σ3 The comparision of yield criteria for a σ2 = 0 plane state of stresses (σ2 = 0) indicates the stress combinations σ1 , σ3 at which flow sets in. kf The curves depicting the yield criteria can -kf thus be considered as an illustration of the −σ1 σ1 flow theory in the σ1 , σ3 plane state of kf stresses. -kf Distortion energy theory (v. Mises) The two flow theories sometimes deliver somewhat different stress values for the −σ3 start of flow. This difference is, however, small and does not exceed 15%. Maximum shear stress theory (Tresca) alu Training in Aluminium Application Technologies 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 σm = (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 ) Important consequences: The logarithmic deformation strain attains the value zero when the corresponding principal stress equals σm. alu Law of Plastic Flow 3303.04.01 Training in Aluminium Application Technologies TALAT 3300 12
  • 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 " "" i.e. kf = f(ϕg, ϕg, ϑ, (ϕg)). 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 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; ϕg n is called strain hardening exponent) alu Flow Curves at Room Temperature (1) 3303.05.02 Training in Aluminium Application Technologies TALAT 3300 13
  • 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 log k f in a coordinate system with axes in a logarithmic scale is a straight line whose gradient is the log k f = n log ϕ g + log a · · coefficient n. The coefficient n is a measure of the amount by which ∆ log k f α a material hardens with increasing deformation strain ϕg and is therefore known as the strain hardening ∆ log ϕ g coefficient. ∆ log k f Typical values of n for an aluminium-killed steel n = tan α = are in the range of ∆ log ϕ g 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) 180 Material Al 99.5 N / mm² " 20°C During forming at elevated temperatures ϕg = 4 s -1 140 120°C (warm forming), the flow stress kf depends on the logarithmic principal deformation strain ϕg , 120 240°C the forming temperature ϑ and the Flow Stress kf 100 logarithmic principal deformation strain rate " (deformation strain rate) ϕg: 80 60 360°C " kf = f(ϕg , ϑ , ϕg) 40 480°C As a rule, the flow stress kf decreases with 20 increasing temperature ϑ for a given logarithmic principal deformation strain ϕg, 0 0.2 0.4 0.6 0.8 1.0 1.2 Logarithmic Principal Deformation Strain ϕg Source: Bühler a.o alu Training in Aluminium Application Technologies Flow Curves at Elevated Temperature (1) 3303.05.04 TALAT 3300 14
  • Flow Curves at Elevated Temperature (2) 100 N / mm² " - With increasing temperature ϑ , the influence ϕg = 63 s -1 of the logarithmic principal deformation strain 80 ϕg on the flow stress kf decreases. Flow Stress kf " ϕg = 4 s -1 60 " " - The influence of the deformation strain rate ϕg ϕg = 0.25 s -1 on the flow stress kf increases with increasing 40 temperature ϑ. For "a given logarithmic principal deformation strain ϕg and a given forming . 20 Material Al 99.5 temperature ϑ, the flow stress kf increases with " Temperature ϑ = 360°C increasing deformation strain rate ϕg. 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) N / mm² 200 20°C 120°C For a given logarithmic principal deformation " strain ϕg and a given forming temperature ϑ, 100 240°C the relationship between the flow stress kf and Flow Stress kf 80 the deformation strain rate ϕg is given 60 approximately by the equation 360°C 40 k f = b ⋅ϕ g m ! C ϕg = 1 480° 20 Material Al 99.5 The exponent m is a measure of the hardening 0.25 40 s-1 63 of the material which depends on the Logarithmic Principal deformation strain rate. " Deformation Strain Rate ϕg It increases with increasing temperature. Source: Bühler a.o alu Training in Aluminium Application Technologies Flow Curves at Elevated Temperature (3) 3303.05.06 TALAT 3300 15
  • 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 kf stress instead of the actual flow stress kfm. For a forming process in the range 0 ≤ ϕg ≤ ϕg1 , it is defined as kf1 kf (ϕg) ϕ g1 ∫k ( ϕ ) dϕ 1 kfm k fm = kf0 ϕ g1 ϕ g1 f g ∫k ( ϕ ) dϕ 0 f g 0 As an approximation, one can use kf 0 + kf 1 k fm = 2 0 ϕg1 ϕg kf0 - flow stress at start of process (ϕg = 0) kf1 - flow stress at end of process (ϕg = ϕg1) alu Average Flow Stress 3303.06.01 Training in Aluminium Application Technologies 3303.07 Energy Considerations Forming Energy (Figure 3303.07.01) Forming Energy Ideal forming energy Total energy (effective forming energy) The ideal forming energy W id is that part of mechanical energy which has to be used for The total forming energy Wges includes the the forming process without external friction ideal forming energy Wid as well as the and internal displacements. energy required to overcome the external friction (WR) and the internal displacement The following relation is valid for the forming (WSch), so that 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 Forming Energy 3303.07.01 TALAT 3300 16
  • 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 Wges ∆ϑ = V * ρ * cp (V formed volume, ρ density and cp specific heat of the work-piece material) alu Training in Aluminium Application Technologies Heat Developed during Forming 3303.07.02 TALAT 3300 17
  • 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 Classifying the Forming Process by State of Stress 3302.02.01 Classifying the Forming Process by Types of Raw Materials 3302.03.01 Classifying the Forming Process by Forming Temperature 3302.04.01 Classifying the Forming Process by Methods of Applying Force 3303.01.01 Characteristic Values, Basic Laws: Flow Stress 3303.02.01 Logarithmic (True) Strain 3303.02.02 Logarithmic Strain in Upsetting 3303.02.03 Law of Volume Constancy 3303.02.04 Plastic Strain Rate (True Strain Rate) 3303.02.05 Forming Strain Acceleration 3303.03.01 Criteria for Plastic Flow 3303.03.02 Shear Stress Hypothesis (1) 3303.03.03 Shear Stress Hypothesis (2) 3303.03.04 Shear Stress Hypothesis (3) 3303.03.05 Distortion Energy Hypothesis (v. Mises) 3303.03.06 Yield Criteria for Plane Stress 3303.04.01 Law of Plastic Flow 3303.05.01 Flow Curve 3303.05.02 Flow Curves at Room Temperature (1) 3303.05.03 Flow Curves at Room Temperature (2) 3303.05.04 Flow Curves at Elevated Temperature (1) 3303.05.05 Flow Curves at Elevated Temperature (2) 3303.05.06 Flow Curves at Elevated Temperature (3) 3303.06.01 Average Flow Stress 3303.07.01 Forming Energy 3303.07.02 Heat Developed during Forming TALAT 3300 18