advances in numerical modeling of manufacturing processes

More documents

Recommendations

Info

TRANS. INDIAN INST. MET., VOL. 57, NO. 4, AUGUST 2004 Fig. 7 : Thermal conductivity and heat capacity of Ti-6Al-4V known that the heat generated inside the workpiece is concentrated along the primary deformation zone and the secondary deformation zones, appearing as thermal energy. A rough estimation of the tool rake face temperature can be obtained using equation 11 34 : 1 2 ⎛ vh ⎞ T f = E⎜ ⎟ (11) ⎝ k ρ c ⎠ where T f is the mean temperature over tool rake face, E is the cutting energy (assuming all cutting energy is converted to heat), k is thermal conductivity, is density, c is specific heat, v is cutting speed, and h is depth of cut. From the above equation it is seen that the thermal properties significantly influence the temperature over the tool/workpiece interface. The temperature varies inversely with the half-power of the change of the product of thermal conductivity k, and heat capacity rc. Thus, higher temperatures are to be expected in cutting stronger materials (high E) at higher speed, especially if the workpiece material is a poor heat conductor of low density, and low specific heat. The density of Ti-6Al-4V can be thought as constant, while the thermal conductivity and specific heat vary with temperature. Both capacity and conductivity increase with temperature 35 . Poor conductivity of the titanium alloys (as compared to steels) results in a larger portion of the heat generated during machining being transferred to the cutting tool, Fig. 8 36 . This leads to high tool temperatures resulting in high tool softening and wear. Fig. 8 : Energy flow rate into tool vs. thermal conductivity of tool 36 . Cutting forces and interface pressure generated during machining are directly proportional to the flow stress of the workpiece material at the representative thermomechanical conditions. During machining the titanium alloy experiences high strains, very high strain rates and temperatures close to its melting point. This results in the following material response: i. Rapid strain hardening at room temperature with strain softening after a peak flow stress is reached (saturation of slip density in the + phase). ii. As the temperature is raised due to heat generation in the primary and secondary shear zones, both the strain hardening and strain softening responses reduce with phase transformations, with almost rigid-perfectly plastic behavior above beta transus. iii. The strain softening of Ti-6Al-4V during deformation varies with the change of microstructure and much more marked flow softening is observed in microstructure compared to the + microstructure. The softening rate depends on the volume fraction of the and phases present below the transus temperature and on the phase above this transus. iv. Strain rate hardening continues at all temperatures with the strain rate sensitivity increasing at higher temperatures. This increase in sensitivity has a major influence on propagation of plastic instability. 352
RAJIV SHIVPURI : NUMERICAL MODELING OF MANUFACTURING PROCESSES v. Reduction in flow stress with increase in temperature (thermal softening) leads to strain localization which in turn causes greater deformation in the localized region. This accumulation of deformation eventually leads to material fracture and the segregated chip. For practical cutting speeds in machining, the average strain rate in the primary shear zone lies in the range of 103 to 105 /s and effective strain can exceed 3.0. The flow stress model should be able to cover this range. In addition, in - titanium alloys, phase transformation to takes place above transus. The original flow stress data are modified on the basis of published sources 37-41 . Detailed information about the flow behavior of Ti-6Al-4V versus temperature and strain rate as well as the flow stress at high strain rate and high temperature can be found in these papers. Consequently, in this study, the flow stress response to changing strain, strain rate and temperature is modified based on the microstructural changes in the deformed chip. The detailed procedure can be found in papers 42, 43 . Figure 9 shows schematically the material model used in this research. The flow localization and the fracture depend on the thermomechanical behavior and the microstructure of the titanium alloy. 3.3 FEM model for orthogonal machining In this research the cutting process is modeled as orthogonal machining. This simplification of geometry and metal flow permits the process to be assumed a 2-dimensional plane strain problem where the movement of the cutting tool is perpendicular to its straight cutting edge. A simplified FEM model for cutting tool, workpiece and interface is illustrated in Fig. 10. Fig. 9 : Flow stress of Ti-6Al-4V as a function of strain, strain rate and temperature. Note the substantial softening at large values of strain at lower temperatures The material for the cutting tool is tungsten carbide (WC/Co) while the workpiece is titanium alloy Ti-6-4. The interface between the chip and tool rake face is modeled by means of an interface heat transfer coefficient and sliding friction factor. The tool geometry, cutting process variables and material properties of tool and coating are listed in Table 1 and Table 2 respectively. Temperature boundary condition on the tool surface is set as follows: a. Constant temperature value of 25 °C is assigned to the nodes on the rake face which are not in 353 Fig. 10: An orthogonal FEM grid model for turning
Page 1 and 2: Trans. Indian Inst. Met. Vol.57, No
Page 3 and 4: RAJIV SHIVPURI : NUMERICAL MODELING
Page 7: RAJIV SHIVPURI : NUMERICAL MODELING

advances in numerical modeling of manufacturing processes

Create successful ePaper yourself

Delete template?

Save as template?