Home Hopkinson rod test results and constitutive description of TRIP780 steel resistance spot welding material
Article Open Access

Hopkinson rod test results and constitutive description of TRIP780 steel resistance spot welding material

  • Xiaomin Li EMAIL logo and Jianrong Zhang
Published/Copyright: December 18, 2020
Download Article (PDF)
Open Physics
From the journal Open Physics Volume 18 Issue 1

Abstract

A quasi-static tensile test was performed on a 1.4 mm-thick TRIP780 steel strip with welding points. An MTS810 material test machine was used in the test, and a Split Hopkinson tension bar device was used in performing impact stretch loading at different strain rates. The dynamic tensile stress–strain curve of the spot welding material with different strain rates was obtained through the finely designed Hopkinson rod test, and the strain rate dependence of a TRIP780 steel spot welding material was discussed. According to the dynamic constitutive equation of the TRIP780 steel spot welding material, the test results were numerically simulated, the constitutive description and test curves were compared, and the simulation results and test results were discussed and analyzed. The fractures of the test recovery specimen were scanned with the scanning electron microscope, and the fracture mechanism of the TRIP780 steel spot welding material was explored by observing the fractures. The surfaces of the fractures surface showed obvious cleavage river patterns, and the evolution process of microcracks was determined and used in characterizing brittle fractures in specimen spot welding sample subjected to dynamic stretch loading.

Keywords: resistance spot welding; impact stretch loading; dynamic constitutive; brittle fracture

1 Introduction

Welding is the most economical and effective method of permanently connecting metals. The dynamic mechanical characteristics of resistance spot welding materials is essential to automobiles, ships, or spacecraft with resistance spot welding structure and under impact load. The dynamic mechanical properties of metals have been at the forefront of research on impact dynamics, and substantial research progress has achieved recently [1,2,3,4,5,6,7,8,9]. Under quasi-static tensile load, research progress [10,11,12,13,14,15,16,17,18,19] of damage evolution can also be popularized and applied to dynamic tensile fractures. The dynamic mechanical properties of steel-based materials have been extensively studied. For example, Oliver et al. [20], Sun et al. [21], and Sung et al. [22] studied the correlation between the strain rate and the failure mode of DP steel. Slycken et al. [23] described the mechanical properties and the phase composition of a TRIP steel under high strain rate loading conditions. Finally, Kang et al. [24], Nicholas [25], and Huh et al. [26] developed and improved the Hopkinson pole tensile test for steel bars. The mechanical behavior of materials has been simulated at high strain rates [27,28].

The quasi-static tensile test was performed on a 1.4 mm-thick TRIP780 steel strip with welding points. An MTS810 material test machine was used in the test. The Split Hopkinson tension bar (SHTB) device was used for impact stretch loading at different strain rates. By using the finely designed Hopkinson rod test, the dynamic tensile stress–strain curve of the spot welding material with different strain rates was obtained, and the strain rate dependence of the welding material was explored. The results of the dynamic tensile test were numerically simulated using the dynamic composition equation of a welding spot material used in our another other study and compared with the stress–strain curve obtained through an experiment. The recovered sample was observed with a scanning electron microscope, and the results of microdamage evolution were obtained. Finally, the fracture pattern of the dynamic tensile fracture of the welding spot material was analyzed.

2 Quasi-static and dynamic tensile test

The TRIP780steel plate was 1.400 mm thick. The time interval between two welding processes was 20 ms, and the welding time and holding time were 130 and 250 ms, respectively. Initially, the welding pressure was 4.300 KN. The quasi-static tensile experiment was carried out on a specimen by using the MTS 810 material test machine, as shown in Figure 1. The quasi-static tensile experiment on TRIP780 steel single-piece specimens was carried out on the same test machine, and a solder pot was used. The stress–strain curve of the welding spot material was obtained, and the specimen and its size and design are shown in Figure 2. Resistance spot welding material was in the middle of the specimen, with a length of 3 mm.

Figure 1 MTS 810 material testing machine.
Figure 1

MTS 810 material testing machine.

Figure 2 Size of the single-piece steel strip specimen with solder joints, unit: mm.
Figure 2

Size of the single-piece steel strip specimen with solder joints, unit: mm.

The quasi-static tensile test stress–strain curve is shown in Figure 3. The front end of the curve is not linear possibly because of a connection problem between the specimen and the loading device, and a relative slip occurs between the specimen and loading device at the start of loading.

Figure 3 Quasi-static tensile stress–strain curve.
Figure 3

Quasi-static tensile stress–strain curve.

The dynamic tensile test of the specimen was performed on the Hopkinson rod. The test device is shown in Figure 4. In the test, the specimen was connected to the incident and transmission bars. When the compressed gas drives a cylinder-shaped projectile with a length of L 0 to hit the target plate at speed V 0 , the cylinder-shaped projectile, incident bar, and transmission bar are all in an elastic state, and the incident and the transmission bars have the same diameter and material, that is, these bars have the same elastic modulus E , wave velocity C 0 , and wave resistance ρ 0 C 0 . Impact produces the incident stress pulse σ I ( t ) load, and the specimen is deformed at high speeds under the loading action of the incident pulse. Reflected stress pulse σ R ( t ) is transmitted to the incident bar, whereas stress pulse σ T ( t ) is transmitted to the transmission bar, which reflects the dynamic mechanical behavior of the test material.

Figure 4 Hopkinson rod test device diagram
Figure 4

Hopkinson rod test device diagram

In the experiment, the diameters of the incident and transmission bars were 19 mm, with lengths of 2.7 and 1.5 m, respectively. The length of the bullet was 300 mm. The incident bar, transmission bar, target plate, and bullet were made of high-strength alloy steel with elastic modulus E of 190 GPa and Poisson ratio ν of 0.3. According to the one-dimensional elastic stress wave theory, in uniform stress and strain, the stress σ ( t ) , strain ε ( t ) , and strain rate ε ̇ ( t ) of the specimen can be calculated using the following equations:

(1) σ ( t ) = A b A 0 E b ε t ( t ) ,

(2) ε ( t ) = − 2 C 0 L 0 ∫ 0 t ε r ( t ) d t ,

(3) ε ̇ ( t ) = − 2 C 0 L 0 ε r ( t ) ,

where t is time; ε t ( t ) and ε r ( t ) are the strain signals of the transmission and reflected waves, respectively; A b and E b are the cross-sectional area and elastic modulus of the incident bar and transmission bar, respectively; C 0 is the elastic wave speed of the rod; and A 0 and L 0 are the cross-sectional area and effective length of the effective segment of the test, respectively. The tensile stress wave was generated after the sleeve bullet travelled through the incident bar, and the surface was reflected when the incident bar and the target plate were free, thus applying multiple tensile loads to the specimen.

The dynamic tensile test stress–strain curve of the specimen at different strain rates is shown in Figure 5. Stress and strain increase with the strain rate although the resulting curve is somewhat irregular. The curve indicates that the spot welding material has a certain strain rate dependence.

Figure 5 Dynamic tensile stress–strain curve.
Figure 5

Dynamic tensile stress–strain curve.

The recycled photographs of the specimen for the quasi-static tensile and Hopkinson rod tests are shown in Figures 6 and 7, respectively. As shown in Figure 6, in the quasi-static tensile experiment, the specimen is sheared and broken, and the fracture is 45°. As shown in Figure 7, the specimen fracture is not an obvious 45° because of dynamic loading.

Figure 6 Recycling specimens under the quasi-static load test.
Figure 6

Recycling specimens under the quasi-static load test.

Figure 7 Recycling specimens under the dynamic tensile test.
Figure 7

Recycling specimens under the dynamic tensile test.

3 Constitutive description

The HV test was performed on the RSW materials of TRIP780 steel. To disclose the HV values of BM, HAZ, and FZ on the RSW material samples, points were set on the left BM and HAZ, center FZ, and right HAZ and BM successively along a biased line that runs through the FZ center. Specifically, points were set horizontally along the center line of BM of the steel plate (1 mm), then turning to the FZ center from the outer edge of HAZ and running through the FZ center and to the horizontal direction of the outer edge of the opposite HAZ (1 mm). The interval between the two points was 0.200 mm. Distribution of the testing points is shown in the dotted line in Figure 8. This study set five points in the right and right BM zones, respectively; four points in the right and right HAZ zones, respectively; and 26 points in the center FZ zone. Therefore, a total of 44 hardness test points in the RSW zone were set.

Figure 8 The RSW cross-sectional micrograph and dot position.
Figure 8

The RSW cross-sectional micrograph and dot position.

For a clear display of the HV hardness values of different parts of the RSW material samples, experimental results and length of RSW material samples were placed in the same coordinate system, and a variation curve of the hardness with length was drawn (Figure 9).

Figure 9 Hardness–length curve.
Figure 9

Hardness–length curve.

In the welding process, bainites in BM are transformed into austenites. With the continuous increase of temperature, ferrites in BM can also be transformed into austenites. Under this circumstance, plastic deformation is developed in the welding zone under spot-welding pressure. With the reduction of temperature, structures are recrystallized and martensitic structures are obtained after cooling. Figure 9 shows that the hardness values of FZ and HAZ are relatively high, whereas that of BM is relatively low. The main reason is that FZ and HAZ are mainly composed of martensites, while BM is mainly composed of ferrites. The hardness values of martensites are higher than those of ferrites. The hardness values of FZ are different from those of HAZ because HAZ components include some residual ferrites relative to the components of FZ, thereby resulting in lower hardness of HAZ than that of FZ. In Figure 9, point S shows the softening point of hardness, which is less than the hardness of wood. The microhardness decreases as the steel plates receive fast thermal circulation at welding.

Roth and Mohr [29] decoupled the strain hardening effect, strain rate hardening effect, and temperature softening effect of materials with reference to the Johnson–Cook constitutive model, thereby obtaining the following dynamic constitutive equation:

(4) σ e BM ( ε p , ε ̇ p , T ) = α A ⁎ ( ε p + ε 0 ) n + ( 1 − α ) k 0 + Q ( 1 − e − β ε p ) × 1 + C ⁎ ln ε ̇ p ε ̇ 0 1 − Δ T T m − T r m ,

where BM refers to the base material; ε p denotes the equivalent plastic strain, ε ̇ p is plastic strain rate, Δ T denotes increase in temperature caused by plastic powers; α is the linear combination coefficient; and k 0 , Q , and β are constants.

The expression of Δ T is

(5) Δ T = η k C p ρ ∫ σ ¯ d ε p ,

where η k is the Taylor–Quinney coefficient, ρ is the mass density, and C p is hot melting.

Model parameters of TRIP780 steel used in constitutive description of a typical experiment are listed in Table 1.

Table 1

The modified Johnson–Cook model parameters for TRIP780 steel used in simulation

A ⁎ (MPa) ε 0 n C ⁎ ε ̇ 0 m
1526.5 0.00519 0.242 0.00557 0.00321 1.025
T r (K) T m (K) E (GPa) ν C p (J/kg K) ρ (kg/m3)
293 1806.7 185 0.33 420 7,850

As the material properties of the welding zone are significantly different from BM in the welding process, we hypothesized that only changes of yield stress in the welding zone are considered in the numerical model, and other mechanical properties and failure parameters are constant in the specimens, as mentioned by Nielsen [30]. It is hypothesized that a linear correlation exists between microhardness and yield stress. Therefore, hardness in the RSW zone is attributed to the hardness of BM. On this basis, the dynamic constitutive equation of the RSW zone of TRIP780 steel is obtained as follows:

(6) σ e RSW ( ε p , ε ̇ p , T ) = λ i σ e BM ( ε p , ε ̇ p , T ) = λ i α A ( ε p + ε 0 ) n + 1 − α ) k 0 + Q 1 − e − β ε p × 1 + C ln ε ̇ p ε ̇ 0 1 − Δ T T m − T r m ,

where RSW represents RSW materials.

We use equation (6) to analyze the results of the dynamic tensile test performed on the specimen. Then, the stress–strain curve was obtained through constitutive description on the basis of the corresponding strain rate and compared with the experimental curve (Figure 10). The comparison results showed that the simulation and experimental results were basically in line with each other but not completely consistent. We believe that this result is related to the dynamic tensile test conditions and processes, including the machining accuracy of the specimen, the closeness of the connection between the specimen and the rod, and the paste quality of the strain gauge, which may have affected the experimental results.

Figure 10 Comparison between experimental results and constitutive description.
Figure 10

Comparison between experimental results and constitutive description.

The fracture of metal material on a microscale is caused by the nucleation, growth, and aggregation of cavities or cracks, which result in ductile or brittle fractures. The increase in the number of cavities or cracks must be aggregated or combined to form a continuous surface and split the specimen. We used an electron microscope to scan a fracture of the dynamic tensile test and the recycling test (Figure 11). By observing the fracture, we observed an obvious cleavage river pattern and the evolution of microcracks. The specimen spot welding part was a brittle fracture.

Figure 11 Scanning electron microscope image of the specimen fracture.
Figure 11

Scanning electron microscope image of the specimen fracture.

4 Conclusion

  1. The quasi-static tensile and Hopkinson rod tests were carried out on TRIP780 steel with solder joints, and the stress–strain curve under the quasi-static tensile was obtained, as well as the stress–strain curve under dynamic tensile at different strain rates. The test results show that the TRIP780 steel spot welding material has a certain strain rate dependence.

  2. The experimental results were numerically simulated using the dynamic material of TRIP780 steel spot welding material obtained. The comparative results show that the constitutive description and test curves were basically in line with the results, and what caused the inconsistence was considered related to the test conditions and processes.

  3. Through electron microscopy and dynamic tensile test, the fractures of the recycled specimen were scanned during the dynamic tensile test. The fracture had an obvious cleavage river pattern, microcrack evolution, and the specimen spot welding part was a brittle fracture.

References

[1] Lubkova E , Yu , Morozov E M , Osintsev A V , Plotnikov A S . On the location of a neck formation during the tension of cylindrical specimens. Lett Mater. 2017;7(3):260–5.10.22226/2410-3535-2017-3-260-265Search in Google Scholar

[2] Verleysen P , Benedict V , Verstraete T , Joris D . Numerical study of the influence of the specimen geometry on split Hopkinson bar tensile test results. Lat Am J Solids Struct. 2009;6:285–98.Search in Google Scholar

[3] Batra RC , Wei ZG . Instability strain and shear band spacing in simple tensile/compressive deformations of thermoviscoplastic materials. Int J Impact Eng. 2007;34:448–63.10.1016/j.ijimpeng.2005.11.004Search in Google Scholar

[4] Tekoglu C , Hutchinson JW , Pardoen T . On localization and void coalescence as a precursor to ductile fracture. Philos Trans R Soc A. 2015;373:2038.10.1098/rsta.2014.0121Search in Google Scholar

[5] Cusumano Joseph P , Arjun R , Qiang L . Damage dynamics, rate laws, and failure statistics via Hamilton’s principle. Meccanica. 2015;50:77–98.10.1007/s11012-014-0055-2Search in Google Scholar

[6] Borja E , Roth Christian C , Dirk M . Stress-state and strain-rate dependent ductile fracture of dual and complex phase steel. Mech Mater. 2018;116:11–32.10.1016/j.mechmat.2017.07.020Search in Google Scholar

[7] Rule WK , Jones SE . A revised form for the Johnson–Cook strength model. Int J Impact Eng. 1998;21(8):609–24.10.1016/S0734-743X(97)00081-XSearch in Google Scholar

[8] Nikhamkin M , Voronov L , Bolotov B . Experimental finding of dynamic deformation fields in metal and composite plates under impact. Pnrpu Mech Bull. 2015;2:103–15.10.15593/perm.mech/2015.2.06Search in Google Scholar

[9] Christian FN . Void growth to coalescence in a non-local material. Eur J Mech-A/Solids. 2008;27(2):222–33.10.1016/j.euromechsol.2007.07.001Search in Google Scholar

[10] Yoshihara H , Yoshinobu M . Nonlinear stress-strain analysis of copy paper under tensile loading by mathematical theory of plasticity. Mokuzai Gakkaishi. 2015;61(2):74–81.10.2488/jwrs.61.74Search in Google Scholar

[11] Bacha A , Daniel D , Klocker H . On the determination of true stress triaxiality in sheet metal. J Mater Process Technol. 2007;184(1–3):272–87.10.1016/j.jmatprotec.2006.11.031Search in Google Scholar

[12] Wooram N , Youngwoo K , Kwansoo C , Jung-Han S , Myoung-Gyu L . Influence of dynamic loading on failure behavior of spot welded automotive steel sheets. Int J Mech Sci. 2018;144:407–26.10.1016/j.ijmecsci.2018.06.009Search in Google Scholar

[13] Fan C , Ma B , Chen D , Deng G , Wang H , Ma D . Uniaxial compression properties of fusion zone martensite in resistance spot-weld for QP980 steel. Weld World. 2019;63:161–6.10.1007/s40194-018-0646-ySearch in Google Scholar

[14] Weck A , Wilkinson DS . Experimental investigation of void coalescence in metallic sheets containing laser drilled holes. Acta Materialia. 2008;56(8):1774–84.10.1016/j.actamat.2007.12.035Search in Google Scholar

[15] Uthaisangsuk V , Prahl U , Münstermann S , Bleck W . Experimental and numerical failure criterion for formability prediction in sheet metal forming. Comput Mater Sci. 2008;43(1):43–50.10.1016/j.commatsci.2007.07.036Search in Google Scholar

[16] Ravindran R , Manonmani K , Narayanasamy R . An analysis of void coalescence in AL 5052 alloy sheets annealed at different temperatures formed under different stress conditions. Mater Sci Eng: A. 2009;507(1–2):252–67.10.1016/j.msea.2009.01.010Search in Google Scholar

[17] Narayanasamy R , Parthasarathi NL , Narayanan CS . Effect of microstructure on void nucleation and coalescence during forming of three different HSLA steel sheets under different stress conditions. Mater Des. 2009;30(4):1310–24.10.1016/j.matdes.2008.06.043Search in Google Scholar

[18] Joun M , Eom JG , Lee M . A new method for acquiring true stress–strain curves over a large range of strains using a tensile test and finite element method. Mech Mater. 2008;40(7):586–93.10.1016/j.mechmat.2007.11.006Search in Google Scholar

[19] Joun M , Choi I , Eom J , Lee M . Finite element analysis of tensile testing with emphasis on necking. Comput Mater Sci. 2007;41(1):63–9.10.1016/j.commatsci.2007.03.002Search in Google Scholar

[20] Oliver S , Jones TB , Fourlaris G . Dual phase versus TRIP strip steels: Microstructural changes as a consequence of quasi-static and dynamic tensile testing. Mater Charact. 2007;58:390–400.10.1016/j.matchar.2006.07.004Search in Google Scholar

[21] Sun X , Choi KS , Liu WN , Khaleel MA . Predicting failure modes and ductility of dual phase steels using plastic strain localization. Int J Plasticity. 2009;25:1888–909.10.1016/j.ijplas.2008.12.012Search in Google Scholar

[22] Sung JH , Kim JH , Wagoner RH . A plastic constitutive equation incorporating strain, strain-rate and temperature. Int J Plasticity. 2010;26:1746–71.10.1016/j.ijplas.2010.02.005Search in Google Scholar

[23] Slycken VJ , Verleysen P , Degrieck J , Bouquerel J , De , Cooman BC . Dynamic response of aluminum containing TRIP steel and its constituent phases. Mater Sci Eng A. 2007;460–461:516–24.10.1016/j.msea.2007.01.075Search in Google Scholar

[24] Kang WJ , Cho SS , Huh H , Chung DT . Identification of dynamic behavior of sheet metals for an auto-body with tension split Hopkinson bar. SAE Trans: J Mater Manuf. 1998;107:908–13. 10.4271/981010Search in Google Scholar

[25] Nicholas T . Tensile testing of materials at high rates of strain. Exp Mech. 1981;21(5):177–85.10.1007/BF02326644Search in Google Scholar

[26] Huh H , Kang WJ , Han SS . A tension split Hopkinson bar for investigating the dynamic behavior of sheet metals. Exp Mech. 2002;42:8–17.10.1007/BF02411046Search in Google Scholar

[27] Wei XC , Fu RY , Li L . Tensile deformation behavior of cold-rolled TRIP-aided steels over large range of strain rates. Mater Sci Eng. 2007;465(1–2):260–6.10.1016/j.msea.2007.02.126Search in Google Scholar

[28] Cao Q , Zhang QD , Sun CY . Constitutive relationship of TRIP780 steel in quenching process. Adv Mater Res. 2012;572:261–6.10.4028/www.scientific.net/AMR.572.261Search in Google Scholar

[29] Roth CC , Mohr D . Effect of strain rate on ductile fracture initiation in advanced high strength sheet. Int J Plasticity. 2014;56:19–44.10.1016/j.ijplas.2014.01.003Search in Google Scholar

[30] Nielsen KL . 3D modelling of plug failure in resistance spot welded shear-lab specimens (DP600-steel). Int J Fract. 2008;153:125–39.10.1007/s10704-008-9305-4Search in Google Scholar
Received: 2020-07-27
Revised: 2020-10-18
Accepted: 2020-10-31
Published Online: 2020-12-18

© 2020 Xiaomin Li and Jianrong Zhang, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

  1. Regular Articles
  2. Model of electric charge distribution in the trap of a close-contact TENG system
  3. Dynamics of Online Collective Attention as Hawkes Self-exciting Process
  4. Enhanced Entanglement in Hybrid Cavity Mediated by a Two-way Coupled Quantum Dot
  5. The nonlinear integro-differential Ito dynamical equation via three modified mathematical methods and its analytical solutions
  6. Diagnostic model of low visibility events based on C4.5 algorithm
  7. Electronic temperature characteristics of laser-induced Fe plasma in fruits
  8. Comparative study of heat transfer enhancement on liquid-vapor separation plate condenser
  9. Characterization of the effects of a plasma injector driven by AC dielectric barrier discharge on ethylene-air diffusion flame structure
  10. Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid
  11. Dependence of the crossover zone on the regularization method in the two-flavor Nambu–Jona-Lasinio model
  12. Novel numerical analysis for nonlinear advection–reaction–diffusion systems
  13. Heuristic decision of planned shop visit products based on similar reasoning method: From the perspective of organizational quality-specific immune
  14. Two-dimensional flow field distribution characteristics of flocking drainage pipes in tunnel
  15. Dynamic triaxial constitutive model for rock subjected to initial stress
  16. Automatic target recognition method for multitemporal remote sensing image
  17. Gaussons: optical solitons with log-law nonlinearity by Laplace–Adomian decomposition method
  18. Adaptive magnetic suspension anti-rolling device based on frequency modulation
  19. Dynamic response characteristics of 93W alloy with a spherical structure
  20. The heuristic model of energy propagation in free space, based on the detection of a current induced in a conductor inside a continuously covered conducting enclosure by an external radio frequency source
  21. Microchannel filter for air purification
  22. An explicit representation for the axisymmetric solutions of the free Maxwell equations
  23. Floquet analysis of linear dynamic RLC circuits
  24. Subpixel matching method for remote sensing image of ground features based on geographic information
  25. K-band luminosity–density relation at fixed parameters or for different galaxy families
  26. Effect of forward expansion angle on film cooling characteristics of shaped holes
  27. Analysis of the overvoltage cooperative control strategy for the small hydropower distribution network
  28. Stable walking of biped robot based on center of mass trajectory control
  29. Modeling and simulation of dynamic recrystallization behavior for Q890 steel plate based on plane strain compression tests
  30. Edge effect of multi-degree-of-freedom oscillatory actuator driven by vector control
  31. The effect of guide vane type on performance of multistage energy recovery hydraulic turbine (MERHT)
  32. Development of a generic framework for lumped parameter modeling
  33. Optimal control for generating excited state expansion in ring potential
  34. The phase inversion mechanism of the pH-sensitive reversible invert emulsion from w/o to o/w
  35. 3D bending simulation and mechanical properties of the OLED bending area
  36. Resonance overvoltage control algorithms in long cable frequency conversion drive based on discrete mathematics
  37. The measure of irregularities of nanosheets
  38. The predicted load balancing algorithm based on the dynamic exponential smoothing
  39. Influence of different seismic motion input modes on the performance of isolated structures with different seismic measures
  40. A comparative study of cohesive zone models for predicting delamination fracture behaviors of arterial wall
  41. Analysis on dynamic feature of cross arm light weighting for photovoltaic panel cleaning device in power station based on power correlation
  42. Some probability effects in the classical context
  43. Thermosoluted Marangoni convective flow towards a permeable Riga surface
  44. Simultaneous measurement of ionizing radiation and heart rate using a smartphone camera
  45. On the relations between some well-known methods and the projective Riccati equations
  46. Application of energy dissipation and damping structure in the reinforcement of shear wall in concrete engineering
  47. On-line detection algorithm of ore grade change in grinding grading system
  48. Testing algorithm for heat transfer performance of nanofluid-filled heat pipe based on neural network
  49. New optical solitons of conformable resonant nonlinear Schrödinger’s equation
  50. Numerical investigations of a new singular second-order nonlinear coupled functional Lane–Emden model
  51. Circularly symmetric algorithm for UWB RF signal receiving channel based on noise cancellation
  52. CH4 dissociation on the Pd/Cu(111) surface alloy: A DFT study
  53. On some novel exact solutions to the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky system arising in physical science
  54. An optimal system of group-invariant solutions and conserved quantities of a nonlinear fifth-order integrable equation
  55. Mining reasonable distance of horizontal concave slope based on variable scale chaotic algorithms
  56. Mathematical models for information classification and recognition of multi-target optical remote sensing images
  57. Hopkinson rod test results and constitutive description of TRIP780 steel resistance spot welding material
  58. Computational exploration for radiative flow of Sutterby nanofluid with variable temperature-dependent thermal conductivity and diffusion coefficient
  59. Analytical solution of one-dimensional Pennes’ bioheat equation
  60. MHD squeezed Darcy–Forchheimer nanofluid flow between two h–distance apart horizontal plates
  61. Analysis of irregularity measures of zigzag, rhombic, and honeycomb benzenoid systems
  62. A clustering algorithm based on nonuniform partition for WSNs
  63. An extension of Gronwall inequality in the theory of bodies with voids
  64. Rheological properties of oil–water Pickering emulsion stabilized by Fe3O4 solid nanoparticles
  65. Review Article
  66. Sine Topp-Leone-G family of distributions: Theory and applications
  67. Review of research, development and application of photovoltaic/thermal water systems
  68. Special Issue on Fundamental Physics of Thermal Transports and Energy Conversions
  69. Numerical analysis of sulfur dioxide absorption in water droplets
  70. Special Issue on Transport phenomena and thermal analysis in micro/nano-scale structure surfaces - Part I
  71. Random pore structure and REV scale flow analysis of engine particulate filter based on LBM
  72. Prediction of capillary suction in porous media based on micro-CT technology and B–C model
  73. Energy equilibrium analysis in the effervescent atomization
  74. Experimental investigation on steam/nitrogen condensation characteristics inside horizontal enhanced condensation channels
  75. Experimental analysis and ANN prediction on performances of finned oval-tube heat exchanger under different air inlet angles with limited experimental data
  76. Investigation on thermal-hydraulic performance prediction of a new parallel-flow shell and tube heat exchanger with different surrogate models
  77. Comparative study of the thermal performance of four different parallel flow shell and tube heat exchangers with different performance indicators
  78. Optimization of SCR inflow uniformity based on CFD simulation
  79. Kinetics and thermodynamics of SO2 adsorption on metal-loaded multiwalled carbon nanotubes
  80. Effect of the inner-surface baffles on the tangential acoustic mode in the cylindrical combustor
  81. Special Issue on Future challenges of advanced computational modeling on nonlinear physical phenomena - Part I
  82. Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications
  83. Some new extensions for fractional integral operator having exponential in the kernel and their applications in physical systems
  84. Exact optical solitons of the perturbed nonlinear Schrödinger–Hirota equation with Kerr law nonlinearity in nonlinear fiber optics
  85. Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water
  86. Closed-form wave structures of the space-time fractional Hirota–Satsuma coupled KdV equation with nonlinear physical phenomena
  87. Some misinterpretations and lack of understanding in differential operators with no singular kernels
  88. Stable solutions to the nonlinear RLC transmission line equation and the Sinh–Poisson equation arising in mathematical physics
  89. Calculation of focal values for first-order non-autonomous equation with algebraic and trigonometric coefficients
  90. Influence of interfacial electrokinetic on MHD radiative nanofluid flow in a permeable microchannel with Brownian motion and thermophoresis effects
  91. Standard routine techniques of modeling of tick-borne encephalitis
  92. Fractional residual power series method for the analytical and approximate studies of fractional physical phenomena
  93. Exact solutions of space–time fractional KdV–MKdV equation and Konopelchenko–Dubrovsky equation
  94. Approximate analytical fractional view of convection–diffusion equations
  95. Heat and mass transport investigation in radiative and chemically reacting fluid over a differentially heated surface and internal heating
  96. On solitary wave solutions of a peptide group system with higher order saturable nonlinearity
  97. Extension of optimal homotopy asymptotic method with use of Daftardar–Jeffery polynomials to Hirota–Satsuma coupled system of Korteweg–de Vries equations
  98. Unsteady nano-bioconvective channel flow with effect of nth order chemical reaction
  99. On the flow of MHD generalized maxwell fluid via porous rectangular duct
  100. Study on the applications of two analytical methods for the construction of traveling wave solutions of the modified equal width equation
  101. Numerical solution of two-term time-fractional PDE models arising in mathematical physics using local meshless method
  102. A powerful numerical technique for treating twelfth-order boundary value problems
  103. Fundamental solutions for the long–short-wave interaction system
  104. Role of fractal-fractional operators in modeling of rubella epidemic with optimized orders
  105. Exact solutions of the Laplace fractional boundary value problems via natural decomposition method
  106. Special Issue on 19th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering
  107. Joint use of eddy current imaging and fuzzy similarities to assess the integrity of steel plates
  108. Uncertainty quantification in the design of wireless power transfer systems
  109. Influence of unequal stator tooth width on the performance of outer-rotor permanent magnet machines
  110. New elements within finite element modeling of magnetostriction phenomenon in BLDC motor
  111. Evaluation of localized heat transfer coefficient for induction heating apparatus by thermal fluid analysis based on the HSMAC method
  112. Experimental set up for magnetomechanical measurements with a closed flux path sample
  113. Influence of the earth connections of the PWM drive on the voltage constraints endured by the motor insulation
  114. High temperature machine: Characterization of materials for the electrical insulation
  115. Architecture choices for high-temperature synchronous machines
  116. Analytical study of air-gap surface force – application to electrical machines
  117. High-power density induction machines with increased windings temperature
  118. Influence of modern magnetic and insulation materials on dimensions and losses of large induction machines
  119. New emotional model environment for navigation in a virtual reality
  120. Performance comparison of axial-flux switched reluctance machines with non-oriented and grain-oriented electrical steel rotors
  121. Erratum
  122. Erratum to “Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications”
https://doi.org/10.1515/phys-2020-0206
Keywords for this article
resistance spot welding; impact stretch loading; dynamic constitutive; brittle fracture
Creative Commons
BY 4.0

Articles in the same Issue

  1. Regular Articles
  2. Model of electric charge distribution in the trap of a close-contact TENG system
  3. Dynamics of Online Collective Attention as Hawkes Self-exciting Process
  4. Enhanced Entanglement in Hybrid Cavity Mediated by a Two-way Coupled Quantum Dot
  5. The nonlinear integro-differential Ito dynamical equation via three modified mathematical methods and its analytical solutions
  6. Diagnostic model of low visibility events based on C4.5 algorithm
  7. Electronic temperature characteristics of laser-induced Fe plasma in fruits
  8. Comparative study of heat transfer enhancement on liquid-vapor separation plate condenser
  9. Characterization of the effects of a plasma injector driven by AC dielectric barrier discharge on ethylene-air diffusion flame structure
  10. Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid
  11. Dependence of the crossover zone on the regularization method in the two-flavor Nambu–Jona-Lasinio model
  12. Novel numerical analysis for nonlinear advection–reaction–diffusion systems
  13. Heuristic decision of planned shop visit products based on similar reasoning method: From the perspective of organizational quality-specific immune
  14. Two-dimensional flow field distribution characteristics of flocking drainage pipes in tunnel
  15. Dynamic triaxial constitutive model for rock subjected to initial stress
  16. Automatic target recognition method for multitemporal remote sensing image
  17. Gaussons: optical solitons with log-law nonlinearity by Laplace–Adomian decomposition method
  18. Adaptive magnetic suspension anti-rolling device based on frequency modulation
  19. Dynamic response characteristics of 93W alloy with a spherical structure
  20. The heuristic model of energy propagation in free space, based on the detection of a current induced in a conductor inside a continuously covered conducting enclosure by an external radio frequency source
  21. Microchannel filter for air purification
  22. An explicit representation for the axisymmetric solutions of the free Maxwell equations
  23. Floquet analysis of linear dynamic RLC circuits
  24. Subpixel matching method for remote sensing image of ground features based on geographic information
  25. K-band luminosity–density relation at fixed parameters or for different galaxy families
  26. Effect of forward expansion angle on film cooling characteristics of shaped holes
  27. Analysis of the overvoltage cooperative control strategy for the small hydropower distribution network
  28. Stable walking of biped robot based on center of mass trajectory control
  29. Modeling and simulation of dynamic recrystallization behavior for Q890 steel plate based on plane strain compression tests
  30. Edge effect of multi-degree-of-freedom oscillatory actuator driven by vector control
  31. The effect of guide vane type on performance of multistage energy recovery hydraulic turbine (MERHT)
  32. Development of a generic framework for lumped parameter modeling
  33. Optimal control for generating excited state expansion in ring potential
  34. The phase inversion mechanism of the pH-sensitive reversible invert emulsion from w/o to o/w
  35. 3D bending simulation and mechanical properties of the OLED bending area
  36. Resonance overvoltage control algorithms in long cable frequency conversion drive based on discrete mathematics
  37. The measure of irregularities of nanosheets
  38. The predicted load balancing algorithm based on the dynamic exponential smoothing
  39. Influence of different seismic motion input modes on the performance of isolated structures with different seismic measures
  40. A comparative study of cohesive zone models for predicting delamination fracture behaviors of arterial wall
  41. Analysis on dynamic feature of cross arm light weighting for photovoltaic panel cleaning device in power station based on power correlation
  42. Some probability effects in the classical context
  43. Thermosoluted Marangoni convective flow towards a permeable Riga surface
  44. Simultaneous measurement of ionizing radiation and heart rate using a smartphone camera
  45. On the relations between some well-known methods and the projective Riccati equations
  46. Application of energy dissipation and damping structure in the reinforcement of shear wall in concrete engineering
  47. On-line detection algorithm of ore grade change in grinding grading system
  48. Testing algorithm for heat transfer performance of nanofluid-filled heat pipe based on neural network
  49. New optical solitons of conformable resonant nonlinear Schrödinger’s equation
  50. Numerical investigations of a new singular second-order nonlinear coupled functional Lane–Emden model
  51. Circularly symmetric algorithm for UWB RF signal receiving channel based on noise cancellation
  52. CH4 dissociation on the Pd/Cu(111) surface alloy: A DFT study
  53. On some novel exact solutions to the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky system arising in physical science
  54. An optimal system of group-invariant solutions and conserved quantities of a nonlinear fifth-order integrable equation
  55. Mining reasonable distance of horizontal concave slope based on variable scale chaotic algorithms
  56. Mathematical models for information classification and recognition of multi-target optical remote sensing images
  57. Hopkinson rod test results and constitutive description of TRIP780 steel resistance spot welding material
  58. Computational exploration for radiative flow of Sutterby nanofluid with variable temperature-dependent thermal conductivity and diffusion coefficient
  59. Analytical solution of one-dimensional Pennes’ bioheat equation
  60. MHD squeezed Darcy–Forchheimer nanofluid flow between two h–distance apart horizontal plates
  61. Analysis of irregularity measures of zigzag, rhombic, and honeycomb benzenoid systems
  62. A clustering algorithm based on nonuniform partition for WSNs
  63. An extension of Gronwall inequality in the theory of bodies with voids
  64. Rheological properties of oil–water Pickering emulsion stabilized by Fe3O4 solid nanoparticles
  65. Review Article
  66. Sine Topp-Leone-G family of distributions: Theory and applications
  67. Review of research, development and application of photovoltaic/thermal water systems
  68. Special Issue on Fundamental Physics of Thermal Transports and Energy Conversions
  69. Numerical analysis of sulfur dioxide absorption in water droplets
  70. Special Issue on Transport phenomena and thermal analysis in micro/nano-scale structure surfaces - Part I
  71. Random pore structure and REV scale flow analysis of engine particulate filter based on LBM
  72. Prediction of capillary suction in porous media based on micro-CT technology and B–C model
  73. Energy equilibrium analysis in the effervescent atomization
  74. Experimental investigation on steam/nitrogen condensation characteristics inside horizontal enhanced condensation channels
  75. Experimental analysis and ANN prediction on performances of finned oval-tube heat exchanger under different air inlet angles with limited experimental data
  76. Investigation on thermal-hydraulic performance prediction of a new parallel-flow shell and tube heat exchanger with different surrogate models
  77. Comparative study of the thermal performance of four different parallel flow shell and tube heat exchangers with different performance indicators
  78. Optimization of SCR inflow uniformity based on CFD simulation
  79. Kinetics and thermodynamics of SO2 adsorption on metal-loaded multiwalled carbon nanotubes
  80. Effect of the inner-surface baffles on the tangential acoustic mode in the cylindrical combustor
  81. Special Issue on Future challenges of advanced computational modeling on nonlinear physical phenomena - Part I
  82. Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications
  83. Some new extensions for fractional integral operator having exponential in the kernel and their applications in physical systems
  84. Exact optical solitons of the perturbed nonlinear Schrödinger–Hirota equation with Kerr law nonlinearity in nonlinear fiber optics
  85. Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water
  86. Closed-form wave structures of the space-time fractional Hirota–Satsuma coupled KdV equation with nonlinear physical phenomena
  87. Some misinterpretations and lack of understanding in differential operators with no singular kernels
  88. Stable solutions to the nonlinear RLC transmission line equation and the Sinh–Poisson equation arising in mathematical physics
  89. Calculation of focal values for first-order non-autonomous equation with algebraic and trigonometric coefficients
  90. Influence of interfacial electrokinetic on MHD radiative nanofluid flow in a permeable microchannel with Brownian motion and thermophoresis effects
  91. Standard routine techniques of modeling of tick-borne encephalitis
  92. Fractional residual power series method for the analytical and approximate studies of fractional physical phenomena
  93. Exact solutions of space–time fractional KdV–MKdV equation and Konopelchenko–Dubrovsky equation
  94. Approximate analytical fractional view of convection–diffusion equations
  95. Heat and mass transport investigation in radiative and chemically reacting fluid over a differentially heated surface and internal heating
  96. On solitary wave solutions of a peptide group system with higher order saturable nonlinearity
  97. Extension of optimal homotopy asymptotic method with use of Daftardar–Jeffery polynomials to Hirota–Satsuma coupled system of Korteweg–de Vries equations
  98. Unsteady nano-bioconvective channel flow with effect of nth order chemical reaction
  99. On the flow of MHD generalized maxwell fluid via porous rectangular duct
  100. Study on the applications of two analytical methods for the construction of traveling wave solutions of the modified equal width equation
  101. Numerical solution of two-term time-fractional PDE models arising in mathematical physics using local meshless method
  102. A powerful numerical technique for treating twelfth-order boundary value problems
  103. Fundamental solutions for the long–short-wave interaction system
  104. Role of fractal-fractional operators in modeling of rubella epidemic with optimized orders
  105. Exact solutions of the Laplace fractional boundary value problems via natural decomposition method
  106. Special Issue on 19th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering
  107. Joint use of eddy current imaging and fuzzy similarities to assess the integrity of steel plates
  108. Uncertainty quantification in the design of wireless power transfer systems
  109. Influence of unequal stator tooth width on the performance of outer-rotor permanent magnet machines
  110. New elements within finite element modeling of magnetostriction phenomenon in BLDC motor
  111. Evaluation of localized heat transfer coefficient for induction heating apparatus by thermal fluid analysis based on the HSMAC method
  112. Experimental set up for magnetomechanical measurements with a closed flux path sample
  113. Influence of the earth connections of the PWM drive on the voltage constraints endured by the motor insulation
  114. High temperature machine: Characterization of materials for the electrical insulation
  115. Architecture choices for high-temperature synchronous machines
  116. Analytical study of air-gap surface force – application to electrical machines
  117. High-power density induction machines with increased windings temperature
  118. Influence of modern magnetic and insulation materials on dimensions and losses of large induction machines
  119. New emotional model environment for navigation in a virtual reality
  120. Performance comparison of axial-flux switched reluctance machines with non-oriented and grain-oriented electrical steel rotors
  121. Erratum
  122. Erratum to “Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications”
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 19.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/phys-2020-0206/html
Scroll to top button