Chapter 4: 金属材料の加工と熱処理

import numpy as np
from scipy.optimize import curve_fit

# 実験データ
strain_exp = np.array([0.1, 0.3])
stress_exp = np.array([300, 420])

# 加工硬化モデル（σ = K * ε^n）
def work_hardening_model(strain, K, n):
    return K * strain**n

# 非線形最小二乗法でパラメータフィット
params, covariance = curve_fit(work_hardening_model, strain_exp, stress_exp,
                                 p0=[500, 0.3])
K_fit, n_fit = params

print("=== Work Hardening Parameter Fitting ===")
print(f"Strength coefficient K = {K_fit:.1f} MPa")
print(f"Work hardening exponent n = {n_fit:.3f}")

# 検証: フィット曲線と実験値の比較
stress_fit = work_hardening_model(strain_exp, K_fit, n_fit)
print("\n=== Verification ===")
for i in range(len(strain_exp)):
    print(f"ε = {strain_exp[i]:.1f}: Experimental σ = {stress_exp[i]} MPa, "
          f"Fitted σ = {stress_fit[i]:.1f} MPa")

# 代数的解法（2点から計算）
# σ1 = K * ε1^n, σ2 = K * ε2^n
# σ2/σ1 = (ε2/ε1)^n → n = log(σ2/σ1) / log(ε2/ε1)
n_algebraic = np.log(stress_exp[1] / stress_exp[0]) / np.log(strain_exp[1] / strain_exp[0])
K_algebraic = stress_exp[0] / (strain_exp[0]**n_algebraic)

print("\n=== Algebraic Solution (2-point method) ===")
print(f"n = log({stress_exp[1]}/{stress_exp[0]}) / log({strain_exp[1]}/{strain_exp[0]}) = {n_algebraic:.3f}")
print(f"K = {stress_exp[0]} / {strain_exp[0]}^{n_algebraic:.3f} = {K_algebraic:.1f} MPa")

# 応力予測（ε = 0.5での値）
strain_pred = 0.5
stress_pred = work_hardening_model(strain_pred, K_fit, n_fit)
print(f"\n=== Prediction ===")
print(f"At ε = {strain_pred}, predicted σ = {stress_pred:.1f} MPa")

期待される出力:

Strength coefficient K ≈ 530-550 MPa
Work hardening exponent n ≈ 0.18-0.20

解説: 2点のデータから、対数を取って連立方程式を解くか、curve_fitで最小二乗フィッティングを行います。\(n\)値が小さい（0.2程度）場合、加工硬化しにくい材料（低炭素鋼など）を示します。

# 銅の融点
T_m_Cu_K = 1358  # Kelvin
T_m_Cu_C = 1085  # Celsius

# 再結晶温度の推定（T_rex ≈ 0.4 * T_m）
T_rex_K = 0.4 * T_m_Cu_K
T_rex_C = T_rex_K - 273.15

print("=== Recrystallization Temperature Estimation ===")
print(f"Melting point of Cu: {T_m_Cu_K} K ({T_m_Cu_C}°C)")
print(f"Estimated recrystallization temperature: {T_rex_K:.0f} K ({T_rex_C:.0f}°C)")

# 応力除去焼鈍温度での判定
stress_relief_temp = 200  # °C

print(f"\n=== Heat Treatment at {stress_relief_temp}°C ===")
if stress_relief_temp < T_rex_C:
    print(f"Temperature ({stress_relief_temp}°C) < T_rex ({T_rex_C:.0f}°C)")
    print("→ Recovery occurs, but NO recrystallization")
    print("→ Stress relief annealing (residual stress reduction)")
else:
    print(f"Temperature ({stress_relief_temp}°C) ≥ T_rex ({T_rex_C:.0f}°C)")
    print("→ Recrystallization occurs")
    print("→ New strain-free grains form, material softens")

# 実用的な熱処理温度範囲
print("\n=== Practical Heat Treatment Ranges for Cu ===")
print(f"Stress relief: {T_rex_C * 0.5:.0f}-{T_rex_C * 0.8:.0f}°C (recovery only)")
print(f"Recrystallization annealing: {T_rex_C:.0f}-{T_rex_C * 1.3:.0f}°C (softening)")
print(f"Homogenization: {T_m_Cu_C * 0.8:.0f}-{T_m_Cu_C * 0.95:.0f}°C (segregation removal)")

期待される出力:

Estimated recrystallization temperature: 543 K (270°C)
At 200°C: Recovery occurs, but NO recrystallization

解説: 再結晶温度は材料により異なりますが、融点の0.3～0.5倍が目安です。銅の場合、約270°C以上で再結晶が生じます。200°Cでは回復（転位の再配列）のみで、結晶粒の再生成は起こりません。

import numpy as np

def calculate_ms_temperature(C, Mn=0, Ni=0, Cr=0):
    """
    マルテンサイト変態開始温度Msの計算（Andrews式）
    Ms = 539 - 423*C - 30.4*Mn - 17.7*Ni - 12.1*Cr
    """
    Ms = 539 - 423*C - 30.4*Mn - 17.7*Ni - 12.1*Cr
    return Ms

# 鋼の化学組成
C_content = 0.6   # wt%
Mn_content = 0.8  # wt%
Ni_content = 0
Cr_content = 0

# Ms温度の計算
Ms_temp = calculate_ms_temperature(C_content, Mn_content, Ni_content, Cr_content)

print("=== Steel Composition ===")
print(f"C: {C_content} wt%, Mn: {Mn_content} wt%, Ni: {Ni_content} wt%, Cr: {Cr_content} wt%")
print(f"\n=== Martensite Start Temperature ===")
print(f"Ms = 539 - 423×{C_content} - 30.4×{Mn_content} - 17.7×{Ni_content} - 12.1×{Cr_content}")
print(f"Ms = {Ms_temp:.1f}°C")

# Mf温度の推定（経験的にMs - 215°C）
Mf_temp = Ms_temp - 215
print(f"Mf (estimated) ≈ {Mf_temp:.1f}°C")

# 水冷の場合
quench_temp_water = 20  # °C
print(f"\n=== Water Quenching (to {quench_temp_water}°C) ===")
if quench_temp_water < Ms_temp:
    martensite_fraction = 100  # 完全マルテンサイト（簡易推定）
    print(f"Final temperature ({quench_temp_water}°C) < Ms ({Ms_temp:.1f}°C)")
    print(f"→ Martensite transformation occurs during quenching")
    print(f"→ Expected structure: ~{martensite_fraction:.0f}% Martensite (high hardness)")
    print(f"→ Hardness: ~60-65 HRC (extremely hard but brittle)")
else:
    print(f"Final temperature ({quench_temp_water}°C) ≥ Ms ({Ms_temp:.1f}°C)")
    print(f"→ Austenite retained (not recommended)")

# 油冷の場合
quench_temp_oil = 60  # °C
print(f"\n=== Oil Quenching (to {quench_temp_oil}°C, then slow cooling) ===")
if quench_temp_oil < Ms_temp:
    # 油冷は水冷より遅いため、一部パーライト/ベイナイト変態の可能性
    print(f"Cooling rate: Slower than water quenching")
    print(f"→ Possible pearlite/bainite transformation at higher temperatures")
    print(f"→ Final structure: Martensite + Bainite (mixed)")
    print(f"→ Hardness: ~50-55 HRC (slightly lower than water quench)")
    print(f"→ Better toughness than full martensite")
else:
    print(f"Final temperature ({quench_temp_oil}°C) ≥ Ms ({Ms_temp:.1f}°C)")
    print(f"→ Austenite may transform to pearlite/bainite")

# 推奨熱処理
print(f"\n=== Recommended Heat Treatment ===")
print(f"1. Austenitizing: 820-850°C, 30-60 min")
print(f"2. Quenching: Oil quench (to avoid cracking)")
print(f"3. Tempering: 200-400°C, 1-2 hours")
print(f"   → Reduces brittleness, improves toughness")
print(f"   → Hardness after tempering: ~45-55 HRC")

# Ms温度への合金元素の影響
print(f"\n=== Effect of Alloying Elements on Ms ===")
elements = {'C': -423, 'Mn': -30.4, 'Ni': -17.7, 'Cr': -12.1}
for elem, coeff in elements.items():
    print(f"{elem}: {coeff:.1f}°C per wt% (negative = lowers Ms)")

期待される出力:

Ms ≈ 261°C
Mf ≈ 46°C
Water quenching: ~100% Martensite (high hardness, brittle)
Oil quenching: Martensite + Bainite (mixed, better toughness)

解説: C 0.6%鋼のMs温度は約260°Cで、室温まで冷却すればマルテンサイトが形成されます。水冷は急冷のためほぼ完全マルテンサイトですが、油冷では冷却速度が遅く、一部ベイナイトが生成される可能性があります。焼入れ後は必ず焼戻しを行い、靭性を向上させることが重要です。

import numpy as np
import matplotlib.pyplot as plt

def calculate_jma_time(X_target, k, n):
    """
    JMA式からターゲット変態率に到達する時間を計算

    X = 1 - exp(-k*t^n)
    → t = (ln(1/(1-X)) / k)^(1/n)

    Parameters:
    -----------
    X_target : float
        目標変態率（0～1）
    k : float
        速度定数 [1/min^n]
    n : float
        Avrami指数

    Returns:
    --------
    t : float
        時間 [min]
    """
    if X_target >= 1.0:
        return np.inf

    t = (np.log(1 / (1 - X_target)) / k)**(1 / n)
    return t

# パラメータ
k = 0.01   # 1/min^n
n = 2.5    # Avrami指数

# 50%再結晶時間
X_50 = 0.5
t_50 = calculate_jma_time(X_50, k, n)

# 90%再結晶時間
X_90 = 0.9
t_90 = calculate_jma_time(X_90, k, n)

print("=== JMA Recrystallization Kinetics ===")
print(f"Parameters: k = {k} (1/min^{n}), n = {n}")
print(f"\n=== Calculation Results ===")
print(f"50% recrystallization time (t_50):")
print(f"  t_50 = (ln(1/(1-{X_50})) / {k})^(1/{n})")
print(f"  t_50 = (ln(2) / {k})^(1/{n})")
print(f"  t_50 = {t_50:.2f} minutes ({t_50/60:.2f} hours)")

print(f"\n90% recrystallization time (t_90):")
print(f"  t_90 = (ln(1/(1-{X_90})) / {k})^(1/{n})")
print(f"  t_90 = (ln(10) / {k})^(1/{n})")
print(f"  t_90 = {t_90:.2f} minutes ({t_90/60:.2f} hours)")

# 時間の比較
ratio = t_90 / t_50
print(f"\n=== Time Ratio ===")
print(f"t_90 / t_50 = {ratio:.2f}")
print(f"→ 90% recrystallization takes {ratio:.2f}× longer than 50%")

# 再結晶曲線のプロット
time = np.linspace(0, t_90 * 1.5, 200)
X = 1 - np.exp(-k * time**n)

plt.figure(figsize=(10, 6))
plt.plot(time, X * 100, 'b-', linewidth=2, label='Recrystallization Curve')
plt.axhline(y=50, color='green', linestyle='--', linewidth=1.5, label=f't_50 = {t_50:.1f} min')
plt.axvline(x=t_50, color='green', linestyle='--', linewidth=1.5, alpha=0.5)
plt.axhline(y=90, color='red', linestyle='--', linewidth=1.5, label=f't_90 = {t_90:.1f} min')
plt.axvline(x=t_90, color='red', linestyle='--', linewidth=1.5, alpha=0.5)

plt.plot(t_50, 50, 'go', markersize=10)
plt.plot(t_90, 90, 'ro', markersize=10)

plt.xlabel('Time [minutes]', fontsize=12)
plt.ylabel('Recrystallized Fraction [%]', fontsize=12)
plt.title(f'JMA Recrystallization Curve (k={k}, n={n})', fontsize=14)
plt.legend(fontsize=11)
plt.grid(True, alpha=0.3)
plt.xlim(0, time[-1])
plt.ylim(0, 100)
plt.tight_layout()
plt.savefig('jma_calculation.png', dpi=300, bbox_inches='tight')
plt.show()

# 異なる変態率での時間計算
print("\n=== Time for Various Recrystallization Fractions ===")
X_values = [0.1, 0.25, 0.5, 0.75, 0.9, 0.95, 0.99]
for X in X_values:
    t = calculate_jma_time(X, k, n)
    print(f"X = {X*100:5.1f}% → t = {t:7.2f} min ({t/60:5.2f} hours)")

期待される出力:

t_50 ≈ 5.28 minutes (0.09 hours)
t_90 ≈ 13.00 minutes (0.22 hours)
t_90 / t_50 ≈ 2.46

解説: JMA式から時間を逆算するには、\(t = [\ln(1/(1-X)) / k]^{1/n}\)を用います。50%変態（\(\ln 2\)）から90%変態（\(\ln 10\)）への時間比は、Avrami指数に依存します。\(n = 2.5\)の場合、約2.46倍の時間がかかります。

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d

# 実験データ
data = {
    150: {'time': [10, 50, 200], 'hardness': [120, 140, 135]},
    175: {'time': [3, 15, 50], 'hardness': [120, 135, 125]},
    200: {'time': [1, 5, 20], 'hardness': [115, 125, 115]}
}

# 最大硬度とピーク時間の決定
print("=== Age Hardening Analysis ===")
print(f"{'Temp [°C]':<12} {'Max Hardness [HV]':<20} {'Peak Time [h]':<15}")
print("-" * 50)

results = {}
for temp, values in data.items():
    times = np.array(values['time'])
    hardness = np.array(values['hardness'])

    max_hardness = np.max(hardness)
    peak_time = times[np.argmax(hardness)]

    results[temp] = {'max_hardness': max_hardness, 'peak_time': peak_time}

    print(f"{temp:<12} {max_hardness:<20} {peak_time:<15}")

# 推奨条件の決定
print("\n=== Recommendation ===")
best_temp = max(results, key=lambda x: results[x]['max_hardness'])
print(f"Best temperature: {best_temp}°C")
print(f"Maximum hardness: {results[best_temp]['max_hardness']} HV")
print(f"Time to peak: {results[best_temp]['peak_time']} hours")

# 実用的な推奨（生産性も考慮）
print("\n=== Practical Recommendation (T6 Treatment) ===")
print(f"Option 1 (Maximum hardness): {best_temp}°C, {results[best_temp]['peak_time']} hours")
print(f"  → Highest hardness ({results[best_temp]['max_hardness']} HV)")
print(f"  → Suitable for maximum strength applications")

print(f"\nOption 2 (Balanced): 175°C, 15 hours")
print(f"  → Good hardness (135 HV, ~96% of max)")
print(f"  → Shorter processing time (3.3× faster than 150°C)")
print(f"  → Better productivity")

print(f"\nOption 3 (Rapid): 200°C, 5 hours")
print(f"  → Moderate hardness (125 HV, ~89% of max)")
print(f"  → Very fast processing (10× faster than 150°C)")
print(f"  → Suitable for rapid production")

# 時効硬化曲線のプロット
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))

# 左図: 実験データと補間曲線
colors = {150: 'blue', 175: 'green', 200: 'red'}
for temp, values in data.items():
    times = np.array(values['time'])
    hardness = np.array(values['hardness'])

    # 補間（cubic spline）
    time_interp = np.linspace(times[0], times[-1], 100)
    f_interp = interp1d(times, hardness, kind='quadratic', fill_value='extrapolate')
    hardness_interp = f_interp(time_interp)

    ax1.plot(time_interp, hardness_interp, color=colors[temp], linewidth=2,
             label=f'{temp}°C', alpha=0.7)
    ax1.plot(times, hardness, 'o', color=colors[temp], markersize=8)

    # ピーク点をマーク
    peak_idx = np.argmax(hardness)
    ax1.plot(times[peak_idx], hardness[peak_idx], '*', color=colors[temp],
             markersize=15, markeredgecolor='black', markeredgewidth=1)

ax1.set_xlabel('Aging Time [hours]', fontsize=12)
ax1.set_ylabel('Hardness [HV]', fontsize=12)
ax1.set_title('Age Hardening Curves for Al-Cu Alloy', fontsize=14)
ax1.legend(fontsize=11)
ax1.grid(True, alpha=0.3)
ax1.set_xscale('log')

# 右図: 最大硬度と到達時間の関係
temps_list = sorted(results.keys())
max_hardness_list = [results[t]['max_hardness'] for t in temps_list]
peak_time_list = [results[t]['peak_time'] for t in temps_list]

ax2_twin = ax2.twinx()
ax2.plot(temps_list, max_hardness_list, 'bo-', linewidth=2, markersize=10,
         label='Max Hardness')
ax2_twin.plot(temps_list, peak_time_list, 'rs-', linewidth=2, markersize=10,
              label='Peak Time')

ax2.set_xlabel('Aging Temperature [°C]', fontsize=12)
ax2.set_ylabel('Maximum Hardness [HV]', fontsize=12, color='blue')
ax2_twin.set_ylabel('Time to Peak [hours]', fontsize=12, color='red')
ax2.tick_params(axis='y', labelcolor='blue')
ax2_twin.tick_params(axis='y', labelcolor='red')
ax2.set_title('Temperature vs. Max Hardness & Peak Time', fontsize=14)
ax2.grid(True, alpha=0.3)

plt.tight_layout()
plt.savefig('age_hardening_analysis.png', dpi=300, bbox_inches='tight')
plt.show()

# 過時効の評価
print("\n=== Over-aging Analysis ===")
for temp in [150, 175, 200]:
    hardness_data = data[temp]['hardness']
    if hardness_data[-1] < max(hardness_data):
        loss = max(hardness_data) - hardness_data[-1]
        loss_pct = (loss / max(hardness_data)) * 100
        print(f"{temp}°C: Over-aging detected (loss = {loss} HV, {loss_pct:.1f}%)")
    else:
        print(f"{temp}°C: No over-aging in observed time range")

期待される出力:

Best temperature: 150°C (Max hardness: 140 HV at 50 hours)
Practical recommendation: 175°C, 15 hours (135 HV, faster processing)
Over-aging detected at all temperatures (hardness decreases after peak)

解説: 低温（150°C）ほど最大硬度は高いですが、到達時間が長くなります。実用的には、175°C・15時間が硬度（135 HV）と生産性のバランスが良い条件です。長時間保持すると過時効により硬度が低下するため、適切な時効時間の管理が重要です。

import numpy as np
import matplotlib.pyplot as plt

# TTT図のパラメータ
Ms_temp = 220  # マルテンサイト変態開始温度 [°C]
pearlite_nose = {'temp': 550, 'time': 1}      # パーライトノーズ [°C, s]
bainite_nose = {'temp': 350, 'time': 10}      # ベイナイトノーズ [°C, s]

# 冷却シナリオ
scenarios = {
    'a': {'cool_time': 1, 'cool_to': 550, 'hold_temp': 550, 'hold_time': 10},
    'b': {'cool_time': 0.1, 'cool_to': 200, 'hold_temp': None, 'hold_time': 0},
    'c': {'cool_time': 10, 'cool_to': 350, 'hold_temp': 350, 'hold_time': 100}
}

def predict_structure(scenario_name, scenario):
    """
    TTT図に基づいて組織を予測
    """
    print(f"\n=== Scenario {scenario_name.upper()} ===")
    print(f"Cooling: {scenario['cool_time']}s to {scenario['cool_to']}°C")
    if scenario['hold_temp']:
        print(f"Holding: {scenario['hold_temp']}°C for {scenario['hold_time']}s")

    cool_time = scenario['cool_time']
    cool_to = scenario['cool_to']
    hold_temp = scenario['hold_temp']
    hold_time = scenario['hold_time']

    # 冷却中の変態判定
    if cool_to == pearlite_nose['temp'] and cool_time >= pearlite_nose['time']:
        print(f"→ Crosses pearlite nose during cooling")
        print(f"→ Partial pearlite transformation likely")
        partial_pearlite = True
    else:
        partial_pearlite = False

    # 保持中の変態判定
    if hold_temp == pearlite_nose['temp'] and hold_time >= pearlite_nose['time']:
        print(f"→ Isothermal holding at pearlite nose temperature")
        print(f"→ COMPLETE pearlite transformation")
        structure = "100% Pearlite"
        hardness = "~20-25 HRC (soft, ductile)"

    elif hold_temp == bainite_nose['temp'] and hold_time >= bainite_nose['time']:
        print(f"→ Isothermal holding at bainite nose temperature")
        print(f"→ COMPLETE bainite transformation")
        structure = "100% Bainite"
        hardness = "~40-50 HRC (moderate hardness, good toughness)"

    elif cool_to < Ms_temp and hold_temp is None:
        print(f"→ Rapid cooling below Ms ({Ms_temp}°C)")
        print(f"→ Martensite transformation")
        structure = "~100% Martensite"
        hardness = "~63-65 HRC (very hard, brittle)"

    else:
        print(f"→ Intermediate cooling")
        if partial_pearlite:
            structure = "Pearlite + Martensite (mixed)"
            hardness = "~35-45 HRC"
        else:
            structure = "Bainite + Martensite (mixed)"
            hardness = "~50-55 HRC"

    print(f"\n【Predicted Structure】: {structure}")
    print(f"【Expected Hardness】: {hardness}")

    return structure, hardness

# 各シナリオの解析
results = {}
for name, scenario in scenarios.items():
    structure, hardness = predict_structure(name, scenario)
    results[name] = {'structure': structure, 'hardness': hardness}

# 結果の比較表
print("\n" + "="*70)
print("=== SUMMARY: Structure Prediction Results ===")
print("="*70)
print(f"{'Scenario':<12} {'Structure':<35} {'Hardness':<20}")
print("-"*70)
for name in ['a', 'b', 'c']:
    print(f"{name.upper():<12} {results[name]['structure']:<35} {results[name]['hardness']:<20}")

# TTT図の簡易プロット（概念図）
fig, ax = plt.subplots(figsize=(12, 8))

# 時間軸（対数）
time = np.logspace(-1, 4, 200)

# パーライト変態曲線（簡易C字型）
P_start = 550 + 150 * (np.log10(time / pearlite_nose['time']))**2
P_start = np.clip(P_start, 400, 727)

# ベイナイト変態曲線
B_start = 350 + 80 * (np.log10(time / bainite_nose['time']))**2
B_start = np.clip(B_start, 250, 500)

ax.semilogx(time, P_start, 'r-', linewidth=2, label='Pearlite Start')
ax.semilogx(time, B_start, 'b-', linewidth=2, label='Bainite Start')
ax.axhline(y=Ms_temp, color='green', linestyle='-', linewidth=2.5, label=f'Ms = {Ms_temp}°C')

# シナリオの冷却曲線をプロット
# Scenario A
cool_time_a = scenarios['a']['cool_time']
hold_time_a = scenarios['a']['hold_time']
time_a = [0, cool_time_a, cool_time_a + hold_time_a]
temp_a = [850, 550, 550]
ax.plot(time_a, temp_a, 'ko-', linewidth=2.5, markersize=8, label='Scenario A', alpha=0.7)

# Scenario B
time_b = [0, scenarios['b']['cool_time']]
temp_b = [850, 200]
ax.plot(time_b, temp_b, 'mo-', linewidth=2.5, markersize=8, label='Scenario B', alpha=0.7)

# Scenario C
cool_time_c = scenarios['c']['cool_time']
hold_time_c = scenarios['c']['hold_time']
time_c = [0, cool_time_c, cool_time_c + hold_time_c]
temp_c = [850, 350, 350]
ax.plot(time_c, temp_c, 'co-', linewidth=2.5, markersize=8, label='Scenario C', alpha=0.7)

ax.set_xlabel('Time [s]', fontsize=13)
ax.set_ylabel('Temperature [°C]', fontsize=13)
ax.set_title('TTT Diagram and Cooling Paths for Eutectoid Steel', fontsize=15, fontweight='bold')
ax.legend(fontsize=11, loc='upper right')
ax.grid(True, alpha=0.3, which='both')
ax.set_xlim(0.1, 1e4)
ax.set_ylim(0, 900)

plt.tight_layout()
plt.savefig('ttt_scenarios.png', dpi=300, bbox_inches='tight')
plt.show()

# 推奨用途
print("\n=== Recommended Applications ===")
print("Scenario A (Pearlite): Rails, wire ropes (high ductility, wear resistance)")
print("Scenario B (Martensite): Cutting tools, bearings (maximum hardness)")
print("Scenario C (Bainite): Gears, springs (balanced hardness and toughness)")

期待される出力:

Scenario A: 100% Pearlite (~20-25 HRC)
Scenario B: ~100% Martensite (~63-65 HRC)
Scenario C: 100% Bainite (~40-50 HRC)

解説: (a)はパーライトノーズ温度で保持するため、完全にパーライト変態します。(b)はMs温度以下まで急冷するため、マルテンサイト組織が得られます。(c)はベイナイトノーズ温度で長時間保持するため、ベイナイト変態が進行します。TTT図上で冷却曲線がどの変態曲線と交わるかを確認することで、組織予測が可能です。