The proposed dynamic fracture based constitutive model

predicted the physical and morphological characteristics of

serrated chip formation in HSM of AISI steel 1045.

It is shown that the ductility of AISI steel 1045 as the work

material can be substantially reduced by applying a certain

combination of the strain rate and negative stress triaxiality. It

sets a foundation for the development of a methodology of

selecting the proper tool geometry and optimal machining

regime.

Reduction of friction at the tool-chip interface may result in:

Improved chip breakability

Up to 25% reduction of the overall energy consumed by

the process

This can be achieved by using tribological coating and/or

metal working fluids of high lubricity.

Abstract

For the first time, serrated chip formation is modeled based

on a novel definition of the metal cutting process as the

purposeful fracture of the layer being removed and the First

and Second Laws of metal cutting. The present work aims to

develop a fracture-based constitutive model of the work

material considering the special loading characteristics of the

orthogonal cutting regime and evaluating the equivalent

fracture strain to be used in the prediction of segmented chip

formation and energy partition in the cutting system. In this

model, both the equivalent strain rate and stress triaxiality

define the material fracture locus. The physical and

morphological characteristics of the chip formation were

analyzed. The anticipated fluctuation of the cutting force

caused by the chip segmentation was observed. The main

objective of the modeling has been formulated – reduction of

plastic deformation of the layer being removed that results in

higher process productivity and efficiency, longer tool life and

better integrity of the machined surface

Material Plasticity Model

General description of a

material plastic flow

Material Damage Model Results

Modeling of Serrated Chip Formation in High Speed Machining: The Fracture Locus Approach

Yalla Abushawashia, Xinran Xiaoa, Viktor Astakhovb a Department of Mechanical Engineering, Michigan State University, E. Lansing, MI, USA

b Production Service Management Inc. (PSMi), Saline, MI, USA

Stress State

Parameterization

Effective strain

Effective strain

Strain rate

σ=f ε g ε h T

σ

ε

T Tempera

ε

ture

n

o

Initial yield strength

Hardening modulus

Strain rate sensitivity

n

εσ= A+Bε 1+

Thermal s

Clnε

A

B

ofte

C

ningFig. 2 JC model optimization for AISI steel 1045

Strain Rate Dependency

Constructing the Plane Strain Fracture Locus with superposition of

hydrostatic stresses to predict damage initiation using flat-grooved

specimen (Bai et al. 2009)

22C η

f 1 1Rice and Tracey model . C and C are the material fracture parε a= sC e meter

Fig.3 Typical 3D fracture locus

(general loading conditions)

Fig.4 Typical 2D Fracture locus

(Specific loading conditions)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

Stre

ss t

riax

ialit

y

Equivalent plastic strain

R12.7-to1.62 R3.97-to1.55

Fig.5 1045 steel plane strain

flat specimens with different

notches (Bai et al. 2009)

Fig.6 Stress triaxiality evolution

diagram of AISI steel 1045

obtained from finite element

simulation for three selected

flat-grooved specimens

Fig. 7 AISI steel 1045 fracture locus based on

initial stress triaxiality, averaged using

displacement limit simulation model, averaged

using strain limit model, and the fracture locus

based on strain at fracture. Stress triaxiality

evolution curves are also shown

0.0

0.2

0.4

0.6

0.8

1.0

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

Equiv

ale

nt s

train

at fr

actu

re

Stress triaxiality parameter

Initial [Wierzbicki, Teng, and Bai] Avg.-disp. limit [Wierzbicki, Teng, and Bai] Avg.-strain limit Strain at fracture

Flat grooved

Tubular specimen

(Tortion test)

0

f

stress state at fractureE d

( , , ) ( , ) ( )f f f f fS R

A modified version of the material

energy density criterion is suggested

to account “indirectly” for material

strain rate sensitivity. It states that

the material toughness in general is

a function of stress state

The general equivalent strain at

fracture is introduced in the following

form

where S is the fracture locus at the

reference equivalent strain rate.

Post Damage Contribution

Damage evolution is assumed to

grow exponentially according to:

The material is assumed to start the

strain softening and degradation

process when the damage indicator

Effe

ctive

str

ess

Effective strain

Dam

age

init

iati

on

Damage Evolution

11

pm

pjc

Conclusions

Fig.10 Serrated chip

simulation in HSM

(Vc=3000m/min, to=0.2mm)

Fig.11 Plastic effective strain

contours in both damaged

and undamaged elements

Fig.12 Stress triaxiality state

contours

Fig. 9 Comparison between the

experimental and modeled

segmented chip morphology. Ref.

(Duan et al. 2010) (cutting speed 432.6m/min, uncut chip thickness to=0.2mm, and rake angle 10o)

Fig. 8 Finite element simulation of the serrated chip formation

with: (a) contact friction, (b) no friction at the tool-chip interface,

and (c) the corresponding cutting force chart

Fig.1 Typical metal stress-strain response

in a uniaxial test

Material plasticity model is represented by a separable function

in terms of the loading condition and uncoupled with the

material degradation beyond damage initiation. This model is

considered as the undamaged hypothetical behavior of the

material.

Reduced form of the Johnson

and Cook model [1]

Predicted Measured Shear angle 27.2deg 31deg peak/valley ratio 1.46 1.41 Chip comp. ratio 1.4 1.43

pf

pc

εp

εf

h

p p

c f

f

1 D=1-exp Lσdε

G

σ= 1-D σ

ε and ε are the eff. plastic strains at the

initiation and fracture site respectively

G is the material fracture energy

L

h

is the element characteristic length

σ is the hypothetic undamaged eff .stress

500

600

700

800

900

0.00 0.10 0.20 0.30 0.40

Effe

ctive

str

ess

Effective plastic strain

Torsion test (Bai et al. 2009)

Johnson and Cook model