MentDB WeakMQL Recipes
← innov-ai.com All profiles Portal
Profiles / Chemistry & life
MS

Materials scientist

Tensile curves, thermal expansion and hardness statistics.

10 recipes on this page · open in the interactive view

Recipes
  1. Young modulus and 0.2 % yield strength from a tensile test
  2. Thermal expansion coefficient and clamped thermal stress
  3. Is a heat treatment really harder? Vickers statistics
  4. Weibull modulus of a ceramic
  5. Fatigue life: Basquin law, Goodman correction and Miner rule
  6. Carburizing time for a given case depth
  7. Hall-Petch law from ASTM grain size numbers
  8. Recrystallization kinetics: JMAK (Avrami) law
  9. Principal stresses and safety factors (Mohr circle)
  10. Cross-ply laminate stiffness by classical lamination theory
executed on MentDB

Young modulus and 0.2 % yield strength from a tensile test

Stress-strain data of a 6061 aluminium sample are fitted with the Ramberg-Osgood law eps = s/E + 0.002.(s/sy)^n, where sy is exactly the 0.2 % offset yield strength Rp0.2. The script returns E, Rp0.2, the hardening exponent n and the permanent set after loading to 290 MPa.

Pipeline
01 · fitRamberg-Osgood non-linear fitstat fit_model→02 · extractE, Rp0.2 and njson select→03 · plasticPlastic strain at 290 MPamath eval
Script
admin
#1. Tensile test of a 6061 aluminium sample: stress in MPa, total strain;
-> "[s]" "[40, 80, 120, 160, 200, 230, 250, 265, 275, 285, 295]";
-> "[eps]" "[0.000575, 0.001162, 0.00175, 0.002312, 0.002881, 0.003407, 0.003972, 0.004834, 0.005816, 0.007634, 0.010951]";
#2. Ramberg-Osgood fit: eps = s/E + 0.002.s/sy^n, sy is the 0.2 % offset yield strength;
json load "rx_ch_ro" (stat fit_model "s/E + 0.002*(s/sy)^n" "s" [s] [eps] "{\"E\": 70000, \"sy\": 270, \"n\": 15}");
-> "[e]" (json select "rx_ch_ro" /parameters/E); -> "[sy]" (json select "rx_ch_ro" /parameters/sy); -> "[n]" (json select "rx_ch_ro" /parameters/n);
#3. Plastic strain left after unloading from 290 MPa;
-> "[ep]" (math eval "0.002*(s/sy)^n" (concat "{\"s\": 290, \"sy\": " [sy] ", \"n\": " [n] "}"));
concat "E = " (math round (math calc "[e]/1000") 1) " GPa, Rp0.2 = " (math round [sy] 1) " MPa, n = " (math round [n] 1) ", permanent set after 290 MPa = " (math round (math calc "100*[ep]") 3) " %"
Result
mentdb
E = 68.8 GPa, Rp0.2 = 276.3 MPa, n = 18.4, permanent set after 290 MPa = 0.486 %
Go further
  • Fit only the elastic part with stat fit "linear" to check E.
  • Compute the strain energy density with num integrate of the fitted curve.
executed on MentDB

Thermal expansion coefficient and clamped thermal stress

A dilatometer measured a 100 mm steel rod from 20 to 400 degC. The script fits L(T) linearly, gives alpha = (dL/dT)/L0 in um/m.K and the thermal stress E.alpha.dT if the rod were fully clamped and heated by 150 K (E = 200 GPa).

Pipeline
01 · fitLinear fit L = a + b.Tstat fit→02 · alphaalpha = b / L0math calc→03 · stresssigma = E.alpha.dT in MPaunit calc
Script
admin
#1. Dilatometer: length of a 100.000 mm steel rod versus temperature in degC;
-> "[t]" "[20, 100, 200, 300, 400]";
-> "[l]" "[100.000, 100.097, 100.219, 100.343, 100.469]";
#2. Linear fit L = a + b.T, alpha = b / L0;
json load "rx_ch_cte" (stat fit [t] [l] "linear");
-> "[alpha]" (math calc (concat (json select "rx_ch_cte" /b) "/100"));
#3. Thermal stress if the rod is fully clamped and heated by 150 K, E = 200 GPa;
-> "[sig]" (unit calc (concat "200 GPa * " [alpha] " * 150") "MPa");
concat "alpha = " (math round (math calc "[alpha]*1e6") 2) " um/m.K, r2 = " (math round (json select "rx_ch_cte" /r2) 5) ", clamped thermal stress = " (math round [sig] 0) " MPa"
Result
mentdb
alpha = 12.34 um/m.K, r2 = 0.99994, clamped thermal stress = 370 MPa
Go further
executed on MentDB

Is a heat treatment really harder? Vickers statistics

Eight HV10 indents were made on two heat treatments of a 42CrMo4 steel. The script gives the mean hardness of B with its 95 % confidence interval, a Welch t-test between A and B, and the usual estimate UTS = 3.3 x HV in MPa.

Pipeline
01 · ciMean and 95 % intervalstat conf_interval_mean→02 · testWelch t-test A vs Bstat ttest_2→03 · utsUTS estimatemath calc
Script
admin
#1. Vickers HV10 indents on two heat treatments of a 42CrMo4 steel;
-> "[a]" "[312, 318, 305, 322, 315, 309, 320, 311]";
-> "[b]" "[331, 326, 338, 329, 335, 324, 333, 330]";
#2. Mean hardness with its 95 % confidence interval;
json load "rx_ch_hv" (stat conf_interval_mean [b] 0.95);
#3. Welch test: is treatment B really harder;
json load "rx_ch_tt" (stat ttest_2 [a] [b]);
#4. Rough tensile strength estimate for steels: UTS = 3.3 x HV in MPa;
concat "HV(B) = " (math round (json select "rx_ch_hv" /mean) 1) " +- " (math round (json select "rx_ch_hv" /margin) 1) ", p = " (json select "rx_ch_tt" /p_value) ", UTS(B) about " (math round (math calc (concat "3.3*" (json select "rx_ch_hv" /mean))) 0) " MPa"
Result
mentdb
HV(B) = 330.8 +- 3.8, p = 0.00002109341984128528, UTS(B) about 1091 MPa
Go further
executed on MentDB

Weibull modulus of a ceramic

Ten alumina bars are broken in flexure. The script builds the Weibull plot in a loop (median ranks), fits the line to get the Weibull modulus with its confidence interval and the scale, then the mean strength with the gamma function and the failure probability at 300 MPa.

Pipeline
01 · plotWeibull plot points in a looppa rl add_data→02 · fitSlope = Weibull moduluspa rl slope→03 · ciConfidence interval and r2pa rl slope_confidence_interval→04 · meanMean strengthgamma(x)
Script
admin
#1. Flexural strength of 10 alumina bars in MPa, sorted;
json load "rx_wb" "{\"s\": [312, 335, 348, 356, 364, 371, 379, 388, 401, 425]}";
#2. Weibull plot: x = ln s, y = ln ln 1/1-F with median ranks F = i-0.3 / n+0.4;
pa rl load_empty "rx_weibull";
for (-> "[i]" 0) (< [i] 10) (++ "[i]") {
  pa rl add_data "rx_weibull" (math calc (concat "ln(" (json select "rx_wb" (concat "/s[" [i] "]")) ")")) (math calc (concat "ln(-ln(1-(" [i] "+0.7)/10.4))"));
};
#3. Weibull modulus m = slope, scale s0 = exp of -intercept/m;
-> "[m]" (pa rl slope "rx_weibull");
-> "[s0]" (math calc (concat "exp(-(" (pa rl intercept "rx_weibull") ")/[m])"));
#4. Mean strength s0 * gamma of 1+1/m, failure probability at 300 MPa;
-> "[r]" (concat "n = " (pa rl count "rx_weibull") ", m = " (math round [m] 1) " +- " (math round (pa rl slope_confidence_interval "rx_weibull") 1) ", r2 = " (math round (pa rl r_square "rx_weibull") 4) ", s0 = " (math round [s0] 1) " MPa, mean = " (math round (math calc "[s0]*gamma(1+1/[m])") 1) " MPa, Pf at 300 MPa = " (math round (math calc "1-exp(-(300/[s0])^[m])") 4));
pa rl close "rx_weibull";
[r]
Result
mentdb
n = 10, m = 12.3 +- 1.4, r2 = 0.9822, s0 = 382.4 MPa, mean = 366.9 MPa, Pf at 300 MPa = 0.0487
Go further
  • Scale to a bigger part with the effective volume: Pf = 1 - exp(-(V/V0) (s/s0)^m).
  • Draw the Weibull plot with plot points.
executed on MentDB

Fatigue life: Basquin law, Goodman correction and Miner rule

Fit the Basquin law to the S-N data of a steel, correct a load block with a mean stress by the Goodman line, get the life at each stress level and sum the Palmgren-Miner damage of one block of the loading spectrum.

Pipeline
01 · basquinsa = sf'.(2Nf)^b, power fitstat fit→02 · goodmansa / (1 - sm/Su)math calc→03 · livesNf = 0.5 (sa/sf')^(1/b)json select→04 · minerD = sum n/Nvector dot
Script
admin
#1. S-N data of a quenched and tempered steel, fully reversed: reversals 2Nf and stress amplitude in MPa;
-> "[rev]" "[2e4, 1e5, 2e5, 1e6, 2e6, 1e7]";
-> "[sa]" "[520, 430, 395, 330, 305, 255]";
#2. Basquin law sa = sf'.2Nf^b, power fit on the log-log line;
json load "rx_tu1_bq" (stat fit [rev] [sa] "power");
-> "[sf]" (json select "rx_tu1_bq" "/a"); -> "[b]" (json select "rx_tu1_bq" "/b");
#3. Block loading: 400 MPa with a mean stress of 100 MPa, Goodman correction with Su = 950 MPa, then 320 and 280 MPa;
-> "[s1]" (math calc "400/(1-100/950)");
-> "[N]" (concat "[" (math calc "0.5*([s1]/[sf])^(1/[b])") ", " (math calc "0.5*(320/[sf])^(1/[b])") ", " (math calc "0.5*(280/[sf])^(1/[b])") "]");
json load "rx_tu1_nf" [N];
#4. Palmgren-Miner damage D = sum n_i/N_i for one block of 2000, 20000 and 100000 cycles;
-> "[inv]" (concat "[" (/ 1 (json select "rx_tu1_nf" "/[0]")) ", " (/ 1 (json select "rx_tu1_nf" "/[1]")) ", " (/ 1 (json select "rx_tu1_nf" "/[2]")) "]");
-> "[D]" (vector dot "[2000, 20000, 100000]" [inv]);
concat "Basquin: sf' = " (math round [sf] 1) " MPa, b = " (math round [b] 4) ", r2 = " (math round (json select "rx_tu1_bq" "/r2") 4) "; Goodman equivalent amplitude = " (math round [s1] 1) " MPa; Nf = " (math round_sig (json select "rx_tu1_nf" "/[0]") 3) ", " (math round_sig (json select "rx_tu1_nf" "/[1]") 3) ", " (math round_sig (json select "rx_tu1_nf" "/[2]") 3) " cycles; damage per block D = " (math round [D] 4) ", blocks to failure = " (math round (/ 1 [D]) 2)
Result
mentdb
Basquin: sf' = 1607.9 MPa, b = -0.1145, r2 = 0.9997; Goodman equivalent amplitude = 447.1 MPa; Nf = 35800, 663000, 2130000 cycles; damage per block D = 0.133, blocks to failure = 7.52
Go further
  • Use the Gerber parabola or the SWT parameter instead of Goodman and compare the damage
  • Count the cycles of a measured load history (rainflow) before applying Miner
executed on MentDB

Carburizing time for a given case depth

Find the gas carburizing time at 930 degC that gives 0.40 %C at 1.0 mm in a 0.20 %C steel with 1.00 %C at the surface (Fick second law, error function), then check the carbon level at 0.5 mm.

Pipeline
01 · diffusionD = D0.exp of -Q/RTmath calc→02 · invertz = erf_inv of the concentration ratiomath erf_inv→03 · timet = x/2z ^2 / Dunit convert→04 · profileC at 0.5 mm with erfcmath erfc
Script
admin
#1. Gas carburizing of a 0.20 %C steel at 930 degC, surface carbon 1.00 %, target 0.40 %C at 1.0 mm;
-> "[cs]" 1.00; -> "[c0]" 0.20; -> "[cx]" 0.40; -> "[x]" 0.001;
#2. Diffusion coefficient of carbon in austenite, D0 = 2.3e-5 m2/s, Q = 148 kJ/mol;
-> "[d]" (math calc "2.3e-5*exp(-148000/(_R*(930+273.15)))");
#3. Fick second law: Cs - Cx / Cs - C0 = erf of x / 2.sqrt Dt, inverted by erf_inv;
-> "[z]" (math erf_inv (math calc "([cs]-[cx])/([cs]-[c0])"));
-> "[t]" (math calc "([x]/(2*[z]))^2/[d]");
#4. Carbon profile check at 0.5 mm after that time: C = C0 + Cs-C0 . erfc;
-> "[c05]" (math calc (concat "[c0]+([cs]-[c0])*" (math erfc (math calc "0.0005/(2*sqrt([d]*[t]))"))));
concat "D = " (math round (math calc "[d]*1e11") 3) "e-11 m2/s, z = " (math round [z] 4) ", carburizing time = " (math round (unit convert [t] "s" "h") 2) " h, carbon at 0.5 mm = " (math round [c05] 3) " %"
Result
mentdb
D = 0.864e-11 m2/s, z = 0.8134, carburizing time = 12.15 h, carbon at 0.5 mm = 0.652 %
Go further
  • Draw the whole carbon profile with plot function and erfc.
  • Add a boost-diffuse cycle by superposition of two solutions.
executed on MentDB

Hall-Petch law from ASTM grain size numbers

Convert ASTM E112 grain size numbers into mean intercept lengths, fit the Hall-Petch law on yield strengths, and find the grain size (and ASTM number) needed to reach 450 MPa.

Pipeline
01 · grainl = 10^-(G+3.298)/6.6457math power→02 · fitsigma_y = sigma0 + k/sqrt dstat fit_model→03 · targetd for 450 MPa, d^-1/2math nroot→04 · astmBack to Gmath log10
Script
admin
#1. Yield strength of a ferritic steel for 4 ASTM E112 grain size numbers G;
-> "[g]" "[5, 7, 9, 11]"; -> "[sy]" "[212, 251, 305, 380]";
#2. Mean lineal intercept l in mm from G: G = -6.6457.log10 l - 3.298;
-> "[l]" (concat "[" (math power 10 (math calc "-(5+3.298)/6.6457")) ", " (math power 10 (math calc "-(7+3.298)/6.6457")) ", " (math power 10 (math calc "-(9+3.298)/6.6457")) ", " (math power 10 (math calc "-(11+3.298)/6.6457")) "]");
#3. Hall-Petch fit: sigma_y = sigma0 + k.d^-1/2, k in MPa.mm^1/2;
json load "rx_p4c_hp" (stat fit_model "s0 + k/sqrt(d)" "d" [l] [sy] "{\"s0\": 100, \"k\": 20}");
-> "[s0]" (json select "rx_p4c_hp" /parameters/s0); -> "[k]" (json select "rx_p4c_hp" /parameters/k);
#4. Grain size needed for 450 MPa, d^-1/2 by a negative root;
-> "[dt]" (math calc "([k]/(450-[s0]))^2");
concat "sigma0 = " (math round [s0] 1) " MPa, k = " (math round [k] 2) " MPa.mm^0.5 (" (math round (math calc "[k]/sqrt(1000)") 3) " MPa.m^0.5), R2 = " (math round (json select "rx_p4c_hp" /r2) 4) "; 450 MPa needs l = " (math round (math calc "[dt]*1000") 2) " um (d^-1/2 = " (math round (math nroot [dt] -2) 2) " mm^-1/2), ASTM G = " (math round (math calc (concat "-6.6457*" (math log10 [dt]) "-3.298")) 1)
Result
mentdb
sigma0 = 120.7 MPa, k = 21.81 MPa.mm^0.5 (0.69 MPa.m^0.5), R2 = 0.9999; 450 MPa needs l = 4.39 um (d^-1/2 = 15.09 mm^-1/2), ASTM G = 12.4
Go further
  • Check the inverse Hall-Petch regime below 20 nm.
  • Add solid-solution and precipitation terms to sigma0.
executed on MentDB

Recrystallization kinetics: JMAK (Avrami) law

Fit the Johnson-Mehl-Avrami-Kolmogorov law on the recrystallized fraction of an annealed aluminium alloy to get the Avrami exponent, then the times for 50 % and 95 % recrystallization.

Pipeline
01 · fitX = 1 - exp of -(k.t)^nstat fit_model→02 · logln 1/(1-X) with log1pmath log1p→03 · timest = ln 1/(1-X) ^1/n / kmath power
Script
admin
#1. Recrystallized fraction of a cold-rolled aluminium alloy annealed at 350 degC, time in s;
-> "[t]" "[60, 120, 180, 300, 450, 600, 900]";
-> "[x]" "[0.03, 0.15, 0.33, 0.66, 0.87, 0.96, 0.995]";
#2. JMAK law X = 1 - exp of -k.t^n;
json load "rx_p4c_av" (stat fit_model "1-exp(-(k*t)^n)" "t" [t] [x] "{\"k\": 0.003, \"n\": 2}");
-> "[k]" (json select "rx_p4c_av" /parameters/k); -> "[n]" (json select "rx_p4c_av" /parameters/n);
#3. Time for 50 % and 95 %: t = ln 1/1-X ^1/n / k, with log1p for accuracy;
-> "[t50]" (math calc (concat (math power (math calc (concat "-" (math log1p -0.5))) (math calc "1/[n]")) "/[k]"));
-> "[t95]" (math calc (concat (math power (math calc (concat "-" (math log1p -0.95))) (math calc "1/[n]")) "/[k]"));
concat "Avrami exponent n = " (math round [n] 2) " , k = " (math round (math calc "[k]*1000") 3) "e-3 1/s; t50 = " (math round [t50] 0) " s, t95 = " (math round [t95] 0) " s, R2 = " (math round (json select "rx_p4c_av" /r2) 4)
Result
mentdb
Avrami exponent n = 1.88 , k = 3.37e-3 1/s; t50 = 244 s, t95 = 532 s, R2 = 0.9982
Go further
  • Repeat at 3 temperatures and fit k with Arrhenius to get the activation energy.
  • An exponent near 2 points to site saturation with 2D growth in a rolled sheet.
executed on MentDB

Principal stresses and safety factors (Mohr circle)

From the plane stress state at a weld toe, compute the Mohr circle, the principal stresses and angle, the maximum shear, and the von Mises and Tresca safety factors.

Pipeline
01 · circleRadius = hypotmath hypot→02 · angletheta_p = 1/2.atan2math atan2→03 · criteriavon Mises and Trescamath calc
Script
admin
#1. Plane stress at a weld toe from a strain rosette, MPa: sigma_x, sigma_y, tau_xy and yield 250 MPa;
-> "[sx]" 120; -> "[sy]" -40; -> "[txy]" 60; -> "[fy]" 250;
#2. Mohr circle: centre and radius = hypot of sx-sy/2 and txy;
-> "[c]" (math calc "([sx]+[sy])/2");
-> "[r]" (math hypot (math calc "([sx]-[sy])/2") [txy]);
#3. Principal stresses and principal angle = 1/2.atan2 of 2.txy and sx-sy;
-> "[s1]" (math calc "[c]+[r]"); -> "[s2]" (math calc "[c]-[r]");
-> "[th]" (math calc (concat "0.5*" (math atan2 (math calc "2*[txy]") (math calc "[sx]-[sy]")) "*180/pi"));
#4. Von Mises and Tresca safety factors, s3 = 0;
-> "[vm]" (math calc "sqrt([s1]^2-[s1]*[s2]+[s2]^2)");
-> "[tr]" (math calc "[s1]-[s2]");
concat "sigma1 = " [s1] " MPa, sigma2 = " [s2] " MPa at " (math round [th] 2) " deg, tau max = " [r] " MPa; von Mises = " (math round [vm] 1) " MPa, SF = " (math round (math calc "[fy]/[vm]") 2) "; Tresca SF = " (math round (math calc "[fy]/[tr]") 2)
Result
mentdb
sigma1 = 140 MPa, sigma2 = -60 MPa at 18.43 deg, tau max = 100 MPa; von Mises = 177.8 MPa, SF = 1.41; Tresca SF = 1.25
Go further
  • Check the result with matrix eigen on the 2x2 stress tensor.
  • Add the fatigue assessment with the stress range and an FAT class.
executed on MentDB

Cross-ply laminate stiffness by classical lamination theory

Build the extensional stiffness matrix A of a 0/90/90/0 carbon-epoxy laminate, factor it once with LU and reuse it for two load cases, then give the effective moduli Ex, nu_xy and Gxy.

Pipeline
01 · plyReduced stiffnesses Q11, Q22, Q12math calc→02 · laminateA = sum Qbar.tmatrix scalar_mul→03 · factorP.A = L.Umatrix lu→04 · strainseps = U^-1.L^-1.P.Nmatrix inverse→05 · moduliEx, nu_xy, Gxymatrix get
Script
admin
#1. Carbon-epoxy ply, GPa: E1 = 140, E2 = 10, G12 = 5, nu12 = 0.3, ply thickness 0.125 mm;
-> "[nu21]" (math calc "0.3*10/140"); -> "[d]" (math calc "1-0.3*[nu21]");
-> "[q11]" (math calc "140/[d]"); -> "[q22]" (math calc "10/[d]"); -> "[q12]" (math calc "0.3*10/[d]");
#2. A = sum of Qbar.t for the cross-ply 0/90/90/0 in GPa.mm, 2 x 0.125 mm at 0 deg and at 90 deg;
-> "[a]" (matrix scalar_mul (concat "[[" (math calc "[q11]+[q22]") ", " (math calc "2*[q12]") ", 0], [" (math calc "2*[q12]") ", " (math calc "[q11]+[q22]") ", 0], [0, 0, 10]]") 0.25);
#3. LU factorization once, reused for two load cases Nx = 100 N/mm and Nxy = 50 N/mm;
json load "rx_p4c_lu" (matrix lu [a]);
-> "[n]" "[[0.1, 0], [0, 0], [0, 0.05]]";
-> "[eps]" (matrix mul (matrix inverse (json select "rx_p4c_lu" /U)) (matrix mul (matrix inverse (json select "rx_p4c_lu" /L)) (matrix mul (json select "rx_p4c_lu" /P) [n])));
#4. Effective moduli of the 0.5 mm laminate: Ex = Nx / h.eps_x, Gxy = Nxy / h.gamma_xy;
concat "eps_x = " (math round (math calc (concat "1e6*" (matrix get [eps] 1 1))) 0) " microstrain, eps_y = " (math round (math calc (concat "1e6*" (matrix get [eps] 2 1))) 0) " microstrain; Ex = " (math round (math calc (concat "0.1/(0.5*" (matrix get [eps] 1 1) ")")) 1) " GPa, nu_xy = " (math round (math calc (concat "-" (matrix get [eps] 2 1) "/" (matrix get [eps] 1 1))) 4) ", Gxy = " (math round (math calc (concat "0.05/(0.5*" (matrix get [eps] 3 2) ")")) 1) " GPa"
Result
mentdb
eps_x = 2654 microstrain, eps_y = -106 microstrain; Ex = 75.4 GPa, nu_xy = 0.04, Gxy = 5 GPa
Go further
  • Add +45/-45 plies with the transformed Qbar (cos and sin of the angle).
  • Compute the ply stresses and a Tsai-Wu failure index.

Also in Chemistry & life

CH
Chemist
Stoichiometry, concentrations, dilutions, pH and gases with real units.
10 recipes
AP
Advanced physical chemist
Kinetics, stiff ODEs, activation energies and equilibria from thermodynamics.
10 recipes
CR
Corrosion researcher
Mass loss, Faraday, Tafel / Stern-Geary, Nernst and Arrhenius lifetimes.
10 recipes
EB
Electrochemist & battery engineer
Nernst, cell energy, Peukert and state of charge.
10 recipes
PR
Process & reactor engineer
Batch and continuous reactors, conversion, residence time and heat of reaction.
10 recipes
PP
Pharmacist & pharmacokinetics
Compartment models, half-life, AUC and dosing regimens.
10 recipes
BM
Biologist & microbiologist
Growth curves, enzyme kinetics and dilution series.
10 recipes
EP
Epidemiologist
Epidemic models, reproduction numbers and incidence statistics: ODE models, growth fits and exact Poisson limits.
10 recipes
GB
Geneticist & bioinformatician
Sequences, allele frequencies and Mendelian risks: regex on DNA, Hardy-Weinberg tests, exact fractions.
10 recipes
MP
Medical physicist
Dose, attenuation, decay correction and image quality: MIRD dose, HVL, dual energy, MTF.
10 recipes
AG
Agronomist
Crop development, fertilization and irrigation: degree days, response curves and rainfall statistics.
10 recipes