31 Oct 2020
12 Aug 2020
Notes on rheology
Using Brookfield rotational viscometer to determine viscosity, shear rate (SR) and shear stress (SS):
Viscosity (P) = Shear stress (D/cm^2) / Shear rate (1/cm)
Viscosity (cP) = TK * SMC * 100/RPM * Torque
TK and SMC are pre-determined constants that depend on the type of viscometer and spindle. TK indicates the selected Spring torque constant and SMC which stands for Spindle Multiplier Constant is a value for the spindle utilised. RPM is the set rotational speed for testing and Torque is a value in %. Refer to the Brookfield rotational viscometer manual for more details.
For an LVDV3T model using a ULA type spindle at 30 RPM and a Torque of 90%, TK = 0.09373 and SMC = 0.64 then:
Viscosity (cP) = 0.09373 * 0.64 * 100/30 * 90 = 17.99616 = 18 cP
Shear rate (1/sec) = SRC * RPM
Shear stress (dynes/cm^2) = TK * SMC * SRC * Torque
where SRC is the Shear rate constant and SMC is the Spindle multiplier constant specific to the spindle type. The user only varies the RPM and Torque, whereas, TK, SMC and SRC values are determined by the viscometer.
Viscosity (P) = Shear stress (D/cm^2) / Shear rate (1/cm)
Viscosity (cP) = TK * SMC * 100/RPM * Torque
TK and SMC are pre-determined constants that depend on the type of viscometer and spindle. TK indicates the selected Spring torque constant and SMC which stands for Spindle Multiplier Constant is a value for the spindle utilised. RPM is the set rotational speed for testing and Torque is a value in %. Refer to the Brookfield rotational viscometer manual for more details.
For an LVDV3T model using a ULA type spindle at 30 RPM and a Torque of 90%, TK = 0.09373 and SMC = 0.64 then:
Viscosity (cP) = 0.09373 * 0.64 * 100/30 * 90 = 17.99616 = 18 cP
Shear rate (1/sec) = SRC * RPM
Shear stress (dynes/cm^2) = TK * SMC * SRC * Torque
where SRC is the Shear rate constant and SMC is the Spindle multiplier constant specific to the spindle type. The user only varies the RPM and Torque, whereas, TK, SMC and SRC values are determined by the viscometer.
For those with zero SRC, the shear rate and shear stress can be calculated manually.
For a RVDV-III type viscometer with a SC4-34 spindle set to operate at 30 RPM (corresponding Torque = 62.3%):
Viscosity (cP) = 1 * 64 * 100/30 * 62.3
Shear rate (1/cm) = 0.28 * 30 = 8.4 sec^-1
Shear stress (dynes/cm^2) = 1 * 64 * 0.28 * 62.3 = 1116.42 dynes/cm^2
Calculation of Viscosity, Shear rate and Shear stress for Cylindrical Spindle where SRC = 0, according to the Brookfield More Solutions handbook:
Shear rate (1/cm) = 2 * ω * Rc^2 * Rb^2 / [X^2 * (RC^2 - Rb^2)]
Shear stress (dynes/cm2) = M / (2 *pi * Rb^2 * L)
Viscosity (Poise) = Shear stress (dynes/cm^2) / Shear rate (1/cm)
where ω is the spindle angular velocity (rad/sec) = 2 * pi / 60 * N (rpm), Rc is the radius of measuring container (cm) and must be no greater than 2Rb, Rb is the Spindle radius (cm), X is the radius of fluid affect by spindle rotation (cm), M is the Torque (%) at specific rpm, L is the Spindle length (cm) affecting viscosity measurement.
The table below shows the radius (cm) Rb for Cylindrical Spindle from the Brookfield handbook. M and X can be determined experimentally but is often assumed to be identical to Rb. L is the effective length below.
For a LVDV-II rotational viscometer with LV1 spindle rotating at 30 rpm with a Torque of 80% (assuming that container inner diameter = 3.768 (= 2Rc) and height = 12.01 cm):
ω (rad/sec) = 2 * pi /60 * 30 = 3.142 rad/sec
Shear rate (1/cm) = 2 * 3.142 * 1.884^2 * 0.9421^2 / [0.9421^2 * (1.884^2 - 0.9421^2)] = 8.3793 sec^-1
Shear stress (dynes/cm^2) = 80 / 2 * pi * 0.9421^2 * 7.493 = 1.9145 dynes/cm^2
Viscosity (Poise) = 1.9145 dynes/cm^2 / 8.3793 sec^-1 = 0.2285 Poise = 22.85 cP
What is the difference between DMA and oscillatory shear rheometry?
Q: Seemingly the data, which we get from a DMA and an oscillatory shear rheometer, is similar (storage modulus, loss modulus, etc.) but are these parameters (G', G'', etc.) the same? I am familiar with the oscillatory shear rheometry but not with DMA. Are we also talking about shear deformation with a DMA?
A: They are usually the same, but some DMA fixtures can also make mechanical testings in the normal direction, such as compression or traction tests (for solids). When a DMA gives you G' and G'', they normally come from an oscillatory shear test performed by the DMA setup.
The G', G", etc you get from oscillatory shear rheometry as well as DMA methods are the same. DMA is usually used when the sample material does not flow easily and hence cannot be sheared between surfaces without slippage. In such cases the DMA set up is used. Most rheometers have the capability to perform DMA measurements as well. However, all rheometers cannot perform all the different kinds of DMA measurements necessary for all materials.
Dynes is the force required to accelerate 1 g of mass by 1 cm/sec^2 (g.cm/sec^2 ).
For a RVDV-III type viscometer with a SC4-34 spindle set to operate at 30 RPM (corresponding Torque = 62.3%):
Viscosity (cP) = 1 * 64 * 100/30 * 62.3
Shear rate (1/cm) = 0.28 * 30 = 8.4 sec^-1
Shear stress (dynes/cm^2) = 1 * 64 * 0.28 * 62.3 = 1116.42 dynes/cm^2
Calculation of Viscosity, Shear rate and Shear stress for Cylindrical Spindle where SRC = 0, according to the Brookfield More Solutions handbook:
Shear rate (1/cm) = 2 * ω * Rc^2 * Rb^2 / [X^2 * (RC^2 - Rb^2)]
Shear stress (dynes/cm2) = M / (2 *pi * Rb^2 * L)
Viscosity (Poise) = Shear stress (dynes/cm^2) / Shear rate (1/cm)
where ω is the spindle angular velocity (rad/sec) = 2 * pi / 60 * N (rpm), Rc is the radius of measuring container (cm) and must be no greater than 2Rb, Rb is the Spindle radius (cm), X is the radius of fluid affect by spindle rotation (cm), M is the Torque (%) at specific rpm, L is the Spindle length (cm) affecting viscosity measurement.
The table below shows the radius (cm) Rb for Cylindrical Spindle from the Brookfield handbook. M and X can be determined experimentally but is often assumed to be identical to Rb. L is the effective length below.
For a LVDV-II rotational viscometer with LV1 spindle rotating at 30 rpm with a Torque of 80% (assuming that container inner diameter = 3.768 (= 2Rc) and height = 12.01 cm):
ω (rad/sec) = 2 * pi /60 * 30 = 3.142 rad/sec
Shear rate (1/cm) = 2 * 3.142 * 1.884^2 * 0.9421^2 / [0.9421^2 * (1.884^2 - 0.9421^2)] = 8.3793 sec^-1
Shear stress (dynes/cm^2) = 80 / 2 * pi * 0.9421^2 * 7.493 = 1.9145 dynes/cm^2
Viscosity (Poise) = 1.9145 dynes/cm^2 / 8.3793 sec^-1 = 0.2285 Poise = 22.85 cP
What is the difference between DMA and oscillatory shear rheometry?
Q: Seemingly the data, which we get from a DMA and an oscillatory shear rheometer, is similar (storage modulus, loss modulus, etc.) but are these parameters (G', G'', etc.) the same? I am familiar with the oscillatory shear rheometry but not with DMA. Are we also talking about shear deformation with a DMA?
A: They are usually the same, but some DMA fixtures can also make mechanical testings in the normal direction, such as compression or traction tests (for solids). When a DMA gives you G' and G'', they normally come from an oscillatory shear test performed by the DMA setup.
The G', G", etc you get from oscillatory shear rheometry as well as DMA methods are the same. DMA is usually used when the sample material does not flow easily and hence cannot be sheared between surfaces without slippage. In such cases the DMA set up is used. Most rheometers have the capability to perform DMA measurements as well. However, all rheometers cannot perform all the different kinds of DMA measurements necessary for all materials.
Dynes is the force required to accelerate 1 g of mass by 1 cm/sec^2 (g.cm/sec^2 ).
1 Poise = g/cm.sec = 100 centiPoise
1 cP = 0.01 P = 0.001 Pa.s = 1 mPa.s (SI unit) known as dynamic viscosity or absolute viscosity.
Kinematic viscosity (centiStoke, cSt or mm^2/s in SI unit) is calculated for Newtonian fluids by dividing absolute viscosity by fluid density = g/cm.sec / g.cm^3 = cm^2/sec.
1 cSt = 0.01 St = 0.000001 m^2/s = 1 mm^2/s
Kinematic viscosity can be measured using Canon Glassware Viscometer (ASTM D445/D446, D2170, D2171).
https://m.blog.naver.com/PostList.nhn?blogId=jiny202040
https://www.researchgate.net/post/What_is_the_difference_between_DMA_and_oscillatory_shear_rheometry
https://m.blog.naver.com/PostList.nhn?blogId=jiny202040
https://www.researchgate.net/post/What_is_the_difference_between_DMA_and_oscillatory_shear_rheometry
3 Aug 2020
Modifying controls parameters in ABAQUS for welding simulation
*CONTROLS option is not needed in most nonlinear analyses, except for use with the parameter ANALYSIS=DISCONTINUOUS. However, if extreme nonlinearities occur, this option may be needed to obtain a solution.
Relaxing the convergence tolerances (which incidentally the ABAQUS manual admits are rather tight) as follows:
Reduce solution times by over 70% in a weld modelling problem with little or no change in the precision of results.
In both the thermal and mechanical analyses, save computation time by specifying more iterations per increment to prevent increments being cut-back, as follows:
*CONTROLS, PARAMETERS=TIME INCREMENTATION
** Relax checks on rate of convergence:** IO IR IP IC IL IG16 , 18 , 20 , 40 , 30 , 6
*CONTROLS, PARAMETERS=FIELD, FIELD=DISPLACEMENT** ... or *CONTROLS, PARAMETERS=FIELD, FIELD=TEMPERATURE** Relax solution tolerances:** R_n^alpha C_n^alpha q_0^alpha q_n^aplha R_p^alpha eps^alpha0.02 , 0.05 , , , 0.10 ,
Slacker tolerances give only very small differences in the solution that are insignificant, given the approximations inherent in weld modelling.
Activating the (normally switched off) line search facility can lead to far fewer cut-backs, particularly those arising from:
'***WARNING: THE STRAIN INCREMENT HAS EXCEEDED FIFTY TIMESTHE STRAIN TO CAUSE FIRST YIELD AT - POINTS'Activate the line search facility as follows:*CONTROLS, PARAMETERS=LINE SEARCH** Nls Smaxls Sminls fsls etals4 , , , ,
Line searching is particularly powerful in the mechanical stress analysis stage of weld modelling where the solution direction is constantly changing. The line search facility obtains a better estimate of the solution at each line search iteration.
For more information see the description of *CONTROLS in the ABAQUS User Manual and the section discussing solution techniques.
Reference
Copy and paste
** CONTROLS***Controls, reset** Relax solution tolerances:** R_n^alpha C_n^alpha q_0^alpha q_n^aplha R_p^alpha eps^alpha*controls, parameters=field0.05, 0.05, , 0.10, 0.05** Relax checks on rate of convergence:** IO IR IP IC IL IG*Controls, parameters=time incrementation16, 18, 20, 40, 30, 6, , 50, , ,*CONTROLS, PARAMETERS=LINE SEARCH** Nls Smaxls Sminls fsls etals4 , , , ,
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