application of the correlation between hardness and strength in conventional Al alloys into semi solid processed products
Kang Du 1,2,a, Wenying Qu 2,b, Yanhong Jing2,cand Qiang Zhu 3,d
1Aluminium Corporation of China, Beijing, China.
2 General Research Institute for Non-Ferrous Metals, Beijing, China
3Department of mechanical and energy engineering, SUST, Shenzhen, China
, ,
Keywords:
aluminum alloy; mechanical strength; hardness; semi-solid castings; molecular mechanics; finite element simulation.
Abstract.
In the field of material production and application, strength and hardness are the two most common propertiesof metallic materials. It’s one familiarphenomenon that the hardness of one certain alloy has positive relationship with its strength in conventional dendritic alloys.When it comes to non-dendritic semi-solid alloys, it’s unclear that the relationship is still right or not.In this paper, the molecular mechanics, as well as finite element simulation and experimental verification were combined to study the internal deformation regularity of metallic material and the correlation between the two parameters was illustrated. Firstly, the displacement of solid atom in metallic crystal cell was well described in the view of energy cost. Secondly, the total strain amount under local indenting deformation (resistant boundary)and overall impressing deformation (free boundary) were comparedto study the correlation between hardness and compression strength in semi-solid globule grain alloy. Finally, the data collected in semi-solid processed products was applied to be compared against traditional casting and wrought aluminum alloys.
1. Introduction
It’s recognized that macro hardness test is one convenient and cheap method to predict the mechanical properties of metallic materials.What’s more, hardness test is also quickerthan tensile testand a nondestructive way to evaluate the stability of commercial production processes.The correlationbetween hardness and tensile strength hasbeen studied for a variety of ferrous materials, nonferrous materials and composite materials [1-3]. Most previous papers presented mainly about the regression analysis based on measured data in one certain alloy, or the influence of microstructure and elements addition on macro properties.A lot of empirical relationships[4-7]has beenreported in bulk metallic glasses, ultra-fine grain materials and particle reinforced composites. The coefficient k ()were concluded to bek≈3.45[4], k≈3[5], k≈2.75[6]or[6], and many other more complicated equations, such ask= [7], [8]where n is one parameter connected with work hardening rateand so on.
In this paper, molecular mechanics calculation, computer aided engineering (CAE) simulation of deformation procedure and real test data collected from literature and own tests were combined to analyze the relationship between hardness and strength of metallic material. Theresults is analyzed in the view of energy consumption and solid atom displacementin plastic deforming. That’s one new idea to study the intrinsic characteristic of metallic materials. Besides, semi-solid techniques is one novelty technique to modify the microstructure from dendritic grains to rosette grains of casting slurry. This change leads to a better filling behavior andformability in casting productions. In the final part of this paper, the different hardness-strength relationships between conventional dendritic alloysand semi-solid alloys will be analyzed.
2. Molecular mechanics analysis
Metals are frequently described by delocalized bondingbecause they are electrical conductors (and thus contain itinerantelectrons) and insulators often by localized bonding since theyare not[9]. Fig.1 is the free electron atmosphere illustration of aluminum crystal cell[10]. Free electron atmosphere model means that no metallic bond would be destroyed even solid atoms move from one node to another.
Fig.1 Illustration of aluminum atom cell and free electron gas
In the molecular mechanics principle[11-13], material strength is one representation of intrinsic energy. The energyexisting in one certain system consists of bond stretch energy (Es), bond angle energy (Eb), torsion bond angle energy (Et,), van der Waal energy (Evdw), electrostatic field energy (Ee) and hydrogen bond energy(Eh)(equation 1). The former three energies are polar interaction while the last three are nonpolarinteractions.
(1)
In metal model, numbers of free electrons form a uniform electron cloud background to keep the electrostatic field stable. Besides, metallic bond is nonpolar interaction, so the energyEs, Eb and Etremain unchanged in plastic deformation process. Hydrogen bond exist in O--H systems was ignored in metallic system.
According to Hu[14]and Batsanov[15]study, the van der Waal radii of aluminum is between 0.202 and 0.238nm. In this paper, we chose the average0.22nm.Transfervan der Waal energy equation into Lennard-Jones Potential equation (2):
(2)
Firstly, calculating the first-order derivative to get the extremum value of B/A(the result is 5.7x10-4nm6). In metallic compound molecular mechanics, no accurate predictionwas generally accepted for both A and B. For more popular issue,such as carbon molecular mechanics, the empirical A is recognized as 5.96x10-3kJ·nm6/mol. In this paper, we choose this value to predict the result of van der Waal energy along the atom displacement in aluminum atom system.
Secondly, introduce the van der Waal radii r0 (0.22nm),and the critical B/A(5.7x10-4nm6) into the above equations to calculate B (the resultis 3.40x10-6kJ·nm12/mol). Meanwhile, and are also been defined.
Finally, in order to get one more vivid contrast of tensile and compressive process, we divided equation (2) into two terms:
r>r0 (3)
r<r0 (4)
Combing the results and equation above, energy change was plotted in Fig.2.
Fig.2 Relationship between solid atom displacement and energy cost in aluminum system
In traditional casting aluminum parts, the elongation is usually below 10%. Assuming in extreme energy cost situation, i.e. the atom layer movement is homogeneous and no defects exist to supply energy. Under the assumption above, the displacement of one atom is 0.0105nm. Poisson ratioυ is 0.33. Once considering the void dislocation and line defects in real metal matrix, the value is much smaller than 0.0105nm. For the x axis value 0.0105nm in Fig.2, the energy contrast is inconspicuous. The energy is respectively 0.6 vs 2.3kJ/mol, i.e.0.1x10-23vs 0.4x10-23kJ/atom. So, the tensile yield strength and compressive yield strength of one alloy is intrinsic different. The difference degree depends on deformation quantity and related to elongation of the material, theoretically. Bigger the atom displacementamount is, more obvious the discrepancy be.
3. Model simulation
In this part, study on the difference between local deformation (hardness test) and overall deformation (compression test) will be focused in cubic cell system which is more similar with semi-solid globule grain but not dendritic grains alloys. Two geometry model were established in finite element method[16].Both of the models have three parts, left die-object-right die. Two dies use the materials of tooling steel. The object is aluminum alloy. The first model (Fig.3 (a)) was used to simulate the hardness test, local indenting process. The second model (Fig.3 (b)) was used to simulate the compression test, overall impressing process. In Fig.3, the big cylinder is φ5mm, the small one is φ1mm. For more simplified model and energy input calculation, the contact surface was set as plane.This point is difference with real spherical indenter.
Fig.3 Geometrymodel for deformation simulation. (a) local indenting hardness test model, (b) overall compressing test model.
The local indenting hardness test and overall compressing test are shown in Fig.4(a) and (b) respectively. It’s shown that the closer the location is to the center, the higher the deformation degree is. The deformation amount at the edge is as little as 10-14 mm which can be ignored.
Fig.4Equivalent total strain of the two modeling (left) local indenting hardness test, and (right) overall compressing test model. Notethat the two dies are hidden.
Based on simulation results, the relationship between energy input and total nodes displacement was illustrated in Fig.5. The black regression line (V1)is the simulation result of overall compressing test while the dashed regression line (V2) is simulation result of local indenting. It’s clear that, under same energy input, V1 is always bigger than V2. It’s means that the overall deformation has easier paths to release energythan local deformation. This explanation also match the red line in Fig.2 well.
What’s more, it’s significant to note that the ratio(V1/V2) is nearly 1.5,constantly. In mechanical properties test field, whatever in hardness test or in tensile strength test, the rule “energy input, deformation output”was eternally immutable. The ratio (V1/V2) relationship could explain the phenomenon that why hardness could be used as one suitable method to predict the tensile properties in metallic material. In this study, the conclusion “ratio between strength and hardness is one constant” was approved in energy view.
Fig.5 Relationship between energy input and total strain in overall compressing simulation (V1), local indenting simulation (V2), and the ratio of the two values
4. Experimental verification of conventional and semi-solid alloys
(a) (b)
Fig.6Relationship betweenhardness and yield strengthin (a) conventional aluminum alloys , (b)semi-solid aluminum alloys and (c) semi-solid 357 alloy
Besides the molecular mechanic calculation and finite element simulation, the existing data[17-19] about hardness and strength in aluminum alloys were collected and plotted in Fig.6(a).(The conversion rule between Vicker hardness and Brinell hardness is ASTM E0140-05) From Fig.6(a), one can see that for both casting and wrought aluminum alloys, the linear relations were obvious. The slops of the two line are 3.5 and 2.6, respectively. Fig.6 (b) is the data comparison of semi-solid alloysagainst conventional casting and wrought alloys. It’s clear that the yield strength of semi-solid casting alloys fall in between that of casting and wrought alloys under same hardness.
In addition, we also studied the evolution of properties ofsemi-solid casting 357 aluminum alloy under different states.The statistical resultsare shown in Fig.6(c). In this plot, it’s concluded that, higher the hardness, smaller the difference between yield and tensile strengthin semi-solid castings.
5. Conclusion
1. The van der Waal energy curve between tensile and compression process is vivid difference. Under same atom displacement, the energy consumption in tensile process is much lower than that incompression process. For globule grain alloy,the energy consumption contrast is 0.6kJ/mol for tension vs 2.3kJ/mol for compression with 10% deformation.
2. In globule grainmodeling, the deformation amount of hardness test (local indentation) is less than compression (total deformation)under same energy input due to less boundary resistance of the latter.In energy point of view,the total strain inoverall compressionis constantly 1.5 timesof that in local indentationunder same energy input.
3. The yield strength of semi-solid alloys falls in between that of the conventional casting and wrought alloys.For the semi-solid casting alloy, higher the hardness, smaller the difference between yield and tensile strength
Acknowledgement
The authors would like to acknowledge the financial support from the National Key Research and Development Program of China (No.2016YFB0301003)
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