Mathematical Modeling on the Residual Stresses in Coatings Due to Heat Treatments

2020 ◽  
Vol 978 ◽  
pp. 514-521
Author(s):  
M.K. Srinath ◽  
M.S. Ganesha Prasad
Keyword(s):  
Residual Stresses ◽  
Coefficient Of Thermal Expansion ◽  
Thermal Strain ◽  
Heat Treatments ◽  
Air Cooling ◽  
Elastic Plastic ◽  
Strain Components ◽  
Cooling Phase ◽  
The Difference ◽  
Plasticity Coefficient

Coatings are implemented on engineering metals and alloys to augment the surface properties such as hardness as well as resistance to wear and corrosion. Heat treatments of coated metals/alloys are performed to aid in the progress of the bonding of the coatings to the substrate. During the air cooling process, the difference in the compositions of the coating and the substrate materials causes them to cool at different rates, which leads to straining in them. The paper presents the research on the mathematical investigation to evaluate the residual stresses in coatings caused due to heat treatments and subsequent air cooling. The mathematical modelling is executed to formulate the equations to represent the residual stresses retained in the coatings due to the heat treatments and subsequent air cooling. Air cooling undergoes two stages namely the initial quenching phase and the final cooling phase. During the quenching phase, the strain was expressed by considering the elastic, plastic and thermal strain components. Poisson’s ratio, deviatoric stress differential of the modulus of plasticity, coefficient of thermal expansion and change in temperature are used to express the elastic, plastic and thermal strain components. During the final cooling phase, the strain was expressed by considering only the elastic and thermal stain components, as the plastic staining the coating material generally does not occur during the final cooling phase and occurs only during the initial quenching phase. From the strain components, the residual stresses for the coatings in the x, y and z axis were formulated. Thus, the total residual stress is the sum total of stresses caused during the initial quenching phase and the final cooling phase.

Effect of Cooling Rate on the Tensile Yield Strength and Ductility Of B2 Compound in Nb-40at.% Ti-15at.%Al Alloy

1993 ◽  
Vol 322 ◽  
Author(s):  
D.-H. Hou ◽  
H.L. Fraser
Keyword(s):  
Heat Treatment ◽  
Tensile Properties ◽  
Cooling Rate ◽  
Heat Treatments ◽  
Water Quenching ◽  
Tensile Yield Strength ◽  
Dominant Factor ◽  
Al Alloy ◽  
Air Cooling ◽  
The Difference

AbstractThe effect of cooling rate on the tensile properties of specimens of the Nb-40Ti-15A1 alloy (in at.%) subjected to various heat treatments has been studied. This alloy has the B2 crystal structure and an order-disorder transition temperature between 1020°C and 1100°C. Two heat treatments have been carried out; the first one involves an 1100°C/1hr heat treatment followed by furnace cooling, air cooling or water quenching. The second type of heat treatment involves re-heating the furnace-cooled and water-quenched specimens at 400°C for 10 minutes or 900°C for 30 minutes, followed by either furnace cooling or water quenching. Tensile properties, SEM fractographs and microstructures of these specimens have been assessed. It is shown that specimens furnace-cooled from 1100°C have higher strength and less ductility than the water quenched ones. An observed microstructural feature associated with cooling rates is the difference in anti-phase domain (APD) size. Discussions are focused on possible cooling rate related phenomena that could affect the tensile properties. It is proposed that the degree of long range ordering, not the APD size, is the dominant factor for the observed cooling rate effect on the tensile properties.

Transient and Residual Stresses and Displacements in Self-Curing Bone Cement—Part I: Characterization of Relevant Volumetric Behavior of Bone Cement

1982 ◽  
Vol 104 (1) ◽  
pp. 21-27 ◽  
Author(s):  
A. M. Ahmed ◽  
W. Pak ◽  
D. L. Burke ◽  
J. Miller
Keyword(s):  
Thermal Expansion ◽  
Residual Stresses ◽  
Bone Cement ◽  
Coefficient Of Thermal Expansion ◽  
Stress Generation ◽  
Curing Process ◽  
Cooling Phase ◽  
Volumetric Behavior ◽  
Fixation System

In this first part of a two-part report, some aspects of the volumetric behavior of bone cement during its curing process are examined as a prelude to an analysis for the transient and residual stresses and displacements in stem fixation systems. Experiments show that stress generation in the cement is associated with its temperature while curing and that during the cooling phase, the stresses are mainly due to thermal as opposed to bulk shrinkage. The appropriate coefficient of thermal expansion of bone cement has been evaluated from measurements in a simulated fixation system in conjunction with a thermoelastic analysis.

Influence of Heat Treatments on Microstructures in an Fe-Co-V Alloy

1974 ◽  
Vol 32 ◽  
pp. 512-513
Author(s):  
S. Mahajan ◽  
M. R. Pinnel ◽  
J. E. Bennett
Keyword(s):  
Single Phase ◽  
Alloy Composition ◽  
Supersaturated Solid Solution ◽  
Cell Formation ◽  
Heat Treatments ◽  
Air Cooling ◽  
Iced Brine ◽  
Transmission Electron ◽  
The Matrix ◽  
Bcc Structure

The microstructural changes in an Fe-Co-V alloy (composition by wt.%: 2.97 V, 48.70 Co, 47.34 Fe and balance impurities, such as C, P and Ni) resulting from different heat treatments have been evaluated by optical metallography and transmission electron microscopy. Results indicate that, on air cooling or quenching into iced-brine from the high temperature single phase ϒ (fcc) field, vanadium can be retained in a supersaturated solid solution (α2) which has bcc structure. For the range of cooling rates employed, a portion of the material appears to undergo the γ-α2 transformation massively and the remainder martensitically. Figure 1 shows dislocation topology in a region that may have transformed martensitically. Dislocations are homogeneously distributed throughout the matrix, and there is no evidence for cell formation. The majority of the dislocations project along the projections of <111> vectors onto the (111) plane, implying that they are predominantly of screw character.

scholarly journals Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 145
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeong-Maw Hwang
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Large Strains ◽  
Rigid Plastic ◽  
Plastic Properties ◽  
Elastic Plastic ◽  
Starting Point ◽  
The Difference ◽  
Inside Radius ◽  
Elastic Unloading

The present paper concerns the general solution for finite plane strain pure bending of incompressible, orthotropic sheets. In contrast to available solutions, the new solution is valid for inhomogeneous distributions of plastic properties. The solution is semi-analytic. A numerical treatment is only necessary for solving transcendent equations and evaluating ordinary integrals. The solution’s starting point is a transformation between Eulerian and Lagrangian coordinates that is valid for a wide class of constitutive equations. The symmetric distribution relative to the center line of the sheet is separately treated where it is advantageous. It is shown that this type of symmetry simplifies the solution. Hill’s quadratic yield criterion is adopted. Both elastic/plastic and rigid/plastic solutions are derived. Elastic unloading is also considered, and it is shown that reverse plastic yielding occurs at a relatively large inside radius. An illustrative example uses real experimental data. The distribution of plastic properties is symmetric in this example. It is shown that the difference between the elastic/plastic and rigid/plastic solutions is negligible, except at the very beginning of the process. However, the rigid/plastic solution is much simpler and, therefore, can be recommended for practical use at large strains, including calculating the residual stresses.

On Thick-Walled Cylinder Under Internal Pressure

2003 ◽  
Vol 125 (3) ◽  
pp. 267-273 ◽  
Author(s):  
W. Zhao ◽  
R. Seshadri ◽  
R. N. Dubey
Keyword(s):  
Internal Pressure ◽  
Strain Curve ◽  
Stress Strain ◽  
Piecewise Linearization ◽  
Elastic Plastic ◽  
Plastic Cylinder ◽  
Parametric Functions ◽  
The Difference ◽  
New Formulation ◽  
Walled Cylinder

A technique for elastic-plastic analysis of a thick-walled elastic-plastic cylinder under internal pressure is proposed. It involves two parametric functions and piecewise linearization of the stress-strain curve. A deformation type of relationship is combined with Hooke’s law in such a way that stress-strain law has the same form in all linear segments, but each segment involves different material parameters. Elastic values are used to describe elastic part of deformation during loading and also during unloading. The technique involves the use of deformed geometry to satisfy the boundary and other relevant conditions. The value of strain energy required for deformation is found to depend on whether initial or final geometry is used to satisfy the boundary conditions. In the case of low work-hardening solid, the difference is significant and cannot be ignored. As well, it is shown that the new formulation is appropriate for elastic-plastic fracture calculations.

Fracture of Layered Ceramics

2009 ◽  
Vol 409 ◽  
pp. 94-106 ◽  
Author(s):  
Raúl Bermejo ◽  
Luca Ceseracciu ◽  
Luis Llanes ◽  
Marc Anglada
Keyword(s):  
Residual Stresses ◽  
Thermal Strain ◽  
Ceramic Materials ◽  
Layered Structures ◽  
Internal Layers ◽  
Multilayered Structures ◽  
Compressive Stresses ◽  
Layered Ceramics ◽  
Different Response ◽  
Experimental Findings

Layered ceramics are foreseen as possible substitutes for monolithic ceramics due to their attractive mechanical properties in terms of strength reliability and toughness. The different loading conditions to which ceramic materials may be subjected in service encourage the design of tailored layered structures as function of their application. The use of residual stresses generated during cooling due to the different thermal strain of adjacent layers has been the keystone for the improvement of the fracture response of many layered ceramic systems, e.g. alumina-zirconia, alumina-mullite, silicon nitride-titanium nitride, etc. In this work, the fracture features of layered ceramics are addressed analysing two multilayered structures, based on the alumina-zirconia system, designed with tailored compressive residual stresses either in the external or internal layers. Contact strength and indentation strength tests have been performed to investigate the response of both designs to crack propagation. The experimental findings show a different response in terms of strength and crack growth resistance of both designs. While layered structures with compressive stresses at the surface provide a better response against contact damage compared to monoliths, a flaw tolerant design in terms of strength and an improved toughness through energy release mechanisms is achieved with internal compressive stresses. The use of layered architectures for automotive or biomedical applications as substitutes for alumina-based ceramics should be regarded in the near future, where reliable ceramic designs are needed.

Recrystallization and Grain Growth during Alloy 718 Processing

2007 ◽  
Vol 539-543 ◽  
pp. 3094-3099
Author(s):  
Nho Kwang Park ◽  
Jeoung Han Kim ◽  
Jong Taek Yeom
Keyword(s):  
Grain Size ◽  
Grain Growth ◽  
Heat Treatments ◽  
Grain Structure ◽  
Alloy 718 ◽  
Compression Tests ◽  
Δ Phase ◽  
Grain Boundary Characteristics ◽  
The Difference ◽  
Boundary Characteristics

In Alloy 718 ingot cogging process, dynamic and metadynamic recrystallizations, and static grain growth occur, and also the presence of δ phase plays a key role in controlling the grain size. In this study, the evolution of grain structure in VIM/VAR-processed Alloy 718 ingots during post-cogging heat treatments is dealt with. Compression tests were made on VIM/VAR-processed Alloy 718 ingot at temperatures between 900oC ~ 1150oC. Heat treatments were made on the compression-tested specimens, and the variation of grain size was evaluated. Constitutive equations for the grain growth are established to represent the evolution of microstructures. Special attention is paid to the evolution of grain structure under the condition of dynamic and metadynamic recrystallizations, and grain growth. The grain growth rate depends mainly on the presence of δ-phase below the δ-solvus temperature, and on the difference in the grain boundary characteristics above it.

scholarly journals Overheating In Silicon During Pulsed-Laser Irradiation?

1985 ◽  
Vol 51 ◽  
Author(s):  
B. C. Larson ◽  
J. Z. Tischler ◽  
D. M. Mills
Keyword(s):  
Laser Irradiation ◽  
Thermal Strain ◽  
Pulsed Laser ◽  
Interface Velocity ◽  
High Energy ◽  
Time Resolved ◽  
Synchrotron Source ◽  
Zero Velocity ◽  
The Difference ◽  
Pulsed Laser Irradiation

ABSTRACTNanosecond resolution time-resolved x-ray diffraction measurements of thermal strain have been used to measure the interface temperatures in silicon during pulsed-laser irradiation. The pulsed-time-structure of the Cornell High Energy Synchrotron Source (CHESS) was used to measure the temperature of the liquid-solid interface of <111> silicon during melting with an interface velocity of 11 m/s, at a time of near zero velocity, and at a regrowth velocity of 6 m/s. The results of these measurements indicate 110 K difference between the temperature of the interface during melting and regrowth, and the measurement at zero velocity shows that most of the difference is associated with undercooling during the regrowth phase.

Influence of Heat Treatment on Characteristic Behavior of Co-Based Alloy Hardfacing Coatings Deposited by Plasma Transferred Arc Welding

2011 ◽  
Vol 462-463 ◽  
pp. 593-598 ◽  
Author(s):  
Hong Xia Deng ◽  
Hui Ji Shi ◽  
Seiji Tsuruoka ◽  
Hui Chen Yu ◽  
Bin Zhong
Keyword(s):  
Residual Stresses ◽  
Vickers Hardness ◽  
Arc Welding ◽  
Steel Substrate ◽  
Heat Treatments ◽  
Material System ◽  
Coating Surface ◽  
Plasma Transferred Arc ◽  
Transferred Arc ◽  
Plasma Transferred Arc Welding

The Plasma transferred arc welding (PTAW) is widely used for hardfacing components exposed to severe conditions. Without post welding heat treatments, large tensile residual stresses remain in the hardfacing coating, which is detrimental. In this paper, a set of post welding heat treatments was evaluated for the heat-resistant steel substrate – Co-based alloy hardfacing coating system. Microstructural and mechanical properties, including the chemical phases of coating surface, the microstructure of coating surface, the Vickers hardness and the residual welding stress, were investigated before and after the heat treatments. Results revealed that during the heat treatments, some elements reprecipitated and the secondary carbide Cr23C6 was formed. After the treatments, a more regular structure and a higher Vickers hardness were obtained. Moreover, the tensile residual stresses in the coating decreased significantly. Therefore, it can be inferred that the post welding heat treatments employed in this paper were proper for this material system.

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