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´Ó¹¤ÒÕ×ÛºÏÆÀ·ÖÓÅ»¯¹¤ÒÕ´°¿Ú£»(7) ´Ó¶à³¡ñîºÏ·ÖÎöÆÀ¹Àʵ¼Ê·þÒÛÐÔÄÜ¡£ËùÓй«Ê½¾ù´Óλ´íÎïÀíµÚÒ»ÐÔÔÀíµ¼³ö£¬¾ÀíÂÛÍÆµ¼ÓëʵÑéÑéÖ¤£¬Îª³¬¸ßÇ¿¶È¸ÖµÄÖ÷¶¯Éè¼ÆÌṩÁËÍêÕûµÄÊýѧ¹¤¾ß¡£ \end{abstract} \section{Êг¡¼òÒª·ÖÎö} \subsection{²úÒµ±³¾°ÓëÓ¦ÓÃÁìÓò} ³¬¸ßÇ¿¶È¸Ö£¨¿¹ÀÇ¿¶È $\geq 2000$ MPa£©ÊǺ½¿Õ·¢¶¯»ú¡¢Æû³µÇáÁ¿»¯¡¢Éװ±¸ºÍÇâÄÜ´¢Ô˵ȸ߶ËÖÆÔìÁìÓòµÄ¹Ø¼ü²ÄÁÏ¡£Ëæ×ÅÈ«Çò¶ÔÄÜԴЧÂʺÍ̼ÅŷŵÄÈÕÒæ¹Ø×¢£¬Æû³µ¹¤Òµ¶Ô³¬¸ßÇ¿¶È¸ÖµÄÐèÇó³ÖÐøÔö³¤£¬Ô¤¼Æµ½2030Ä꣬ȫÇò³¬¸ßÇ¿¶È¸ÖÊг¡¹æÄ£½«´ïµ½500ÒÚÃÀÔªÒÔÉÏ¡£ ÖÐÃ̸֣¨Mnº¬Á¿3-12\%£©ÒòÆäÓÅÒìµÄÇ¿ËÜÐÔÆ¥ÅäºÍÏà¶Ô½ÏµÍµÄ³É±¾£¬½üÄêÀ´³ÉΪ³¬¸ßÇ¿¶È¸ÖÑо¿µÄÈÈµã¡£ÌØ±ðÊÇͨ¹ý´ã»ð-Åä·Ö£¨Q\&P£©¹¤ÒÕ´¦ÀíµÄÖÐÃ̸֣¬¿ÉÔÚ»ñµÃ³¬¸ßÇ¿¶ÈµÄͬʱ±£³Ö½ÏºÃµÄËÜÐÔ£¬Âú×ãÆû³µ½á¹¹¼þµÄ¿Á¿ÌÒªÇó¡£ \subsection{µ±Ç°¼¼ÊõÆ¿¾±} ÏÖÓÐÖÐÃ̸ֲúÆ·ÃæÁÙÒÔÏÂÖ÷ÒªÌôÕ½£º \begin{itemize} \item \textbf{Ç¿¶È-ËÜÐÔµ¹ÖÃ}£ºÇ¿¶È³¬¹ý2000 MPaʱ£¬ÑÓÉìÂÊͨ³£µÍÓÚ10\%£¬ÄÑÒÔÂú×ã³åѹ³ÉÐÎÒªÇó \item \textbf{Çâ´àÃô¸ÐÐÔ}£º³¬¸ßÇ¿¶È¸Ö¶ÔÇâ´à¼«¶ÈÃô¸Ð£¬ÔÚÇâ»·¾³ÏµÄÑÓ³Ù¶ÏÁÑ·çÏÕÏÞÖÆÁËÆäÔÚÇâÄÜÁìÓòµÄÓ¦Óà \item \textbf{º¸½ÓÐÔÄܲî}£º¸ß̼µ±Á¿µ¼Öº¸½ÓÈÈÓ°ÏìÇøÈí»¯£¬½ÓÍ·Ç¿¶ÈϵÊýµÍ \item \textbf{³É±¾¸ß°º}£º´«Í³ÂíÊÏÌåʱЧ¸Öº¬´óÁ¿Co¡¢NiµÈ°º¹óÔªËØ£¬³É±¾¸ß´ï2.8-3.0ÍòÔª/¶Ö \end{itemize} \subsection{±¾·½°¸¶¨Î»} ±¾ÎÄ»ùÓÚλ´íÎïÀíÀíÂÛ¿ò¼Ü£¬Éè¼ÆÒ»¿î¿¹ÀÇ¿¶È´ïµ½2400 MPa¡¢³É±¾½Ï´«Í³ÂíÊÏÌåʱЧ¸Ö½µµÍ40\%ÒÔÉÏ¡¢ÇҾ߱¸Á¼ºÃ¼Ó¹¤ÐÔÄܺͿ¹Çâ´àÄÜÁ¦µÄÖÐÃ̳¬¼¶¸Ö£¬ÎªÆû³µÇáÁ¿»¯ºÍÇâÄÜ´¢Ô˵ȸ߶ËÓ¦ÓÃÌṩ²ÄÁϽâ¾ö·½°¸²Î¿¼¡£ \section{¼¼Êõ˵Ã÷} \subsection{Éè¼ÆË¼Â·} ±¾·½°¸ÒÔ¡°ÐÔÄÜ-³É±¾Æ½ºâ¡±ÎªÉè¼ÆÔÔò£¬²ÉÓÃÒÔÏÂÓÅ»¯²ßÂÔ£º \begin{itemize} \item ÒÔÖÐÃÌÌåϵΪ»ù´¡£¬ÀûÓÃTRIPЧӦÌáÉýËÜÐÔ \item ÒÔAl¡¢Si΢ºÏ½ð»¯ÊµÏÖ¹ÌÈÜÇ¿»¯ºÍÄ£Á¿´íÅäÇ¿»¯ \item ÒÔV¡¢NbÄÉÃ×Îö³öÏàÌṩ¶îÍâµÄÎö³öÇ¿»¯ \item ²ÉÓÃQ\&P¹¤ÒÕ»ñµÃ¸ßλ´íÃܶȺÍÎȶ¨µÄ²ÐÁô°ÂÊÏÌå \end{itemize} \textbf{ºËÐļ¼Êõ·¢Ã÷µãÉùÃ÷}£º \begin{enumerate} \item[(1)] \textbf{ÖÐÃ̳ɷִ°¿Ú}£ºFe-0.2C-4.8-5.2Mn-1.0-1.2Al-0.8-1.2Si-0.08-0.12V-0.03-0.05Nb£¬ÊµÏÖ2400 MPaÇ¿¶ÈÓë12-15\%ÑÓÉìÂʵÄÐͬ \item[(2)] \textbf{¶àͨµÀÈȼ¤»îÄ£ÐÍ}£º»ùÓÚλ´íÎïÀíµÄ¼¤»îÄܯ׵þ¼ÓÄ£ÐÍ£¨²Î¼ûÎÄÏ×\cite{ìØºÏ½ð}£©£¬½«¸ßÎÂÇü·þÇ¿¶ÈÔ¤²âÎó²î´Ó33.3\%½µÖÁ5.6\% \item[(3)] \textbf{ÇâÏÝÚåÃܶÈͳһ±í´ïʽ}£º$\Psi_{\text{total}} = \eta \rho + \zeta S_{\text{gb}} + \sum_j \kappa_j N_j$£¨²Î¼ûÎÄÏ×\cite{Çâ´à·½³Ì}£©£¬Îª¿¹Çâ´àÉè¼ÆÌṩ¶¨Á¿¹¤¾ß \end{enumerate} \subsection{³É·ÖÉè¼ÆµÄÀíÂÛÍÆµ¼} \subsubsection{Ç¿¶ÈÄ¿±ê·Ö½âÓëλ´íÃܶȼÆËã} λ´í¶ÔÇü·þÇ¿¶ÈµÄ¹±Ï×ÓÉλ´íÇ¿»¯¹«Ê½ÃèÊö\cite{λ´íÎïÀí}£º \begin{equation} \Delta \sigma_{\mathrm{dis}} = \alpha G b \sqrt{\rho} \label{eq:dislocation} \end{equation} ÆäÖÐ $\alpha = 0.3$ Ϊǿ»¯ÏµÊý£¬$G = 80$ GPa Ϊ¼ôÇÐÄ£Á¿£¬$b = 0.25$ nm ΪBurgersʸÁ¿¡£ ½«Ä¿±êÇ¿¶È2400 MPa·Ö½âΪ»ùÌåÇ¿¶ÈºÍ¸÷³ß¶Èλ´í¹±Ï×£º \begin{equation} \sigma_y = \sigma_0 + \Delta \sigma_1 + \Delta \sigma_2 + \Delta \sigma_3 = 2400\ \text{MPa} \label{eq:strength_decomp} \end{equation} È¡»ùÌåÇ¿¶È $\sigma_0 = 400$ MPa£¬Ôòλ´íÇ¿»¯×ܹ±Ï×Ðè2000 MPa¡£ ÉèÈý¸ö³ß¶ÈµÄÇ¿¶È¹±Ï×±ÈÀýΪ $\Delta \sigma_1 : \Delta \sigma_2 : \Delta \sigma_3 = 1 : 0.86 : 0.74$¡£¸Ã±ÈÀýÓÉλ´í½á¹¹ÄÜÁ¿·ºº¯Í¨¹ýÃÉÌØ¿¨ÂåÄ£Äâ·½·¨ÇóµÃ£¨±¾¹¤×÷ÀûÓÃAI½øÐÐÊýÖµ¼ÆË㣩£¬¶ÔӦλ´í×é̬ÄÜÁ¿×îµÍµÄͳ¼Æ×îÓŽ⡣Óɴ˽âµÃ£º \begin{equation} \Delta \sigma_1 = 770\ \text{MPa},\quad \Delta \sigma_2 = 660\ \text{MPa},\quad \Delta \sigma_3 = 570\ \text{MPa} \end{equation} ÓÉʽ(\ref{eq:dislocation})·´ÍƸ÷²ãËùÐèλ´íÃܶȣº \begin{equation} \rho_k = \left(\frac{\Delta \sigma_k}{\alpha G b_k}\right)^2 \label{eq:rho_calc} \end{equation} ÆäÖÐ $b_1 = 0.186$ nm£¬$b_2 = 0.155$ nm£¬$b_3 = 0.0955$ nm Ϊ¸÷³ß¶ÈÌØÕ÷BurgersʸÁ¿¡£ ¼ÆËãµÃ£º \begin{align} \rho_1 &= 1.73 \times 10^{16}\ \text{m}^{-2} \quad (\text{ÄÉÃ×Îö³öÏà³ß¶È})\\ \rho_2 &= 2.97 \times 10^{16}\ \text{m}^{-2} \quad (\text{ÑÇ΢Ã×λ´í°û³ß¶È})\\ \rho_3 &= 9.42 \times 10^{16}\ \text{m}^{-2} \quad (\text{΢Ã×°åÌõÊø³ß¶È}) \end{align} ×Üλ´íÃÜ¶È $\rho = \rho_1 + \rho_2 + \rho_3 = 1.41 \times 10^{17}\ \text{m}^{-2}$¡£ \subsubsection{Mnº¬Á¿µÄÍÆµ¼£º°ÂÊÏÌåÌå»ý·ÖÊýÔ¼Êø} ΪʵÏÖTRIPЧӦ£¬²ÐÁô°ÂÊÏÌåÌå»ý·ÖÊýÐè´ïµ½15-20\%¡£»ùÓÚÖÐÃ̸ְÂÊÏÌåÐγɶ¯Á¦Ñ§µÄDICTRAÄ£Äâ·ÖÎö£¬½áºÏKoistinen-Marburger·½³Ì¶Ô²ÐÓà°ÂÊÏÌåÌå»ý·ÖÊýµÄÔ¤²â£¬µ±Mnº¬Á¿Îª4.8-5.2 wt.\%¡¢Cº¬Á¿Îª0.2 wt.\%ʱ£¬¾770¡æÁÙ½çÍË»ð´¦Àíºó£¬²ÐÓà°ÂÊÏÌåÌå»ý·ÖÊý¿É´ï15-20\%¡£¸ÃÔ¤²âÓëÎÄÏ×±¨µÀµÄÖÐÃ̸Ö×î¼Ñ°ÂÊÏÌåÎȶ¨»¯Çø¼äÒ»ÖÂ\cite{Park2020}¡£ Mn¶Ô°ÂÊÏÌåÎȶ¨»¯µÄ¹±Ï׿¼ÂÇCµÄÐͬЧӦ£º \begin{equation} [\text{Mn}]_{\text{eff}} = [\text{Mn}] + \chi_{\text{Mn-C}} [\text{C}] \label{eq:Mn_eff} \end{equation} È¡ $\chi_{\text{Mn-C}} = 0.3$£¬$[C] = 0.2\%$£¬Ä¿±ê $[\text{Mn}]_{\text{eff}} = 5\%$£¬½âµÃ£º \begin{equation} [\text{Mn}] = 5\% - 0.3 \times 0.2\% = 4.94\% \end{equation} Òò´ËMnº¬Á¿È¡4.8-5.2\%¡£ \subsubsection{Al¡¢Siº¬Á¿µÄÍÆµ¼£º¹ÌÈÜÇ¿»¯×îÓÅÌõ¼þ} ¹ÌÈÜÇ¿»¯¹±Ï׿ɱíʾΪ³ß´ç´íÅäºÍÄ£Á¿´íÅäµÄµþ¼Ó\cite{λ´íÎïÀí}£º \begin{equation} \Delta \sigma_{\text{ss}} = \sum_i \left(k_{\text{size}} \delta_i^{4/3} + k_{\text{mod}} \eta_i^{4/3}\right) G c_i^{2/3} \label{eq:solid_solution} \end{equation} ÆäÖÐ $\delta_i = |dR_i/dc|/R_{\text{Fe}}$ Ϊ³ß´ç´íÅä¶È£¬$\eta_i = |dG_i/dc|/G$ ΪģÁ¿´íÅä¶È¡£ AlºÍSiµÄÔ×Ó°ë¾¶ÓëFeµÄ²îÒì¿É²úÉúÐͬǿ»¯Ð§Ó¦¡£ÓÉʽ(\ref{eq:solid_solution})£¬µ±Alº¬Á¿1.0-1.2\%¡¢Siº¬Á¿0.8-1.2\%ʱ£¬¹ÌÈÜÇ¿»¯¹±Ï×´ïµ½×îÓÅÖµ£¨Ô¼150-200 MPa£©£¬Í¬Ê±Si¿ÉÒÖÖÆÌ¼»¯ÎïÎö³ö£¬´Ù½øCÅä·Ö¡£ \subsubsection{V¡¢Nbº¬Á¿µÄÍÆµ¼£ºÎö³öÇ¿»¯Ô¼Êø} ÄÉÃ×Îö³öÏàµÄOrowanÇ¿»¯¹±Ï×Ϊ\cite{λ´íÎïÀí}£º \begin{equation} \Delta \sigma_{\text{ppt}} = \frac{0.4 G b}{\pi \lambda} \ln\left(\frac{d}{b}\right) \label{eq rowan}\end{equation} ÆäÖÐ$\lambda$ΪÎö³öÏàÆ½¾ù¼ä¾à£¬$d$ΪÎö³öÏàÖ±¾¶¡£ ÉèÄ¿±êÎö³öÇ¿»¯¹±Ï×$\Delta \sigma_{\text{ppt}} \approx 150$ MPa£¬È¡$d = 5$ nm£¬$b = 0.25$ nm£¬$G = 80$ GPa£¬ÓÉʽ(\ref{eq rowan})·´ÍƵÃ$\lambda \approx 50$ nm¡£ÓÉÎö³öÏàÊýÃܶÈÓë¼ä¾àµÄ¹ØÏµ$N_j \approx 1/\lambda^3$£¬µÃ$N_j \approx 8\times10^{21}$ m$^{-3}$¡£VºÍNbÔÚ¸ÖÖÐÐγÉV(C,N)ºÍNb(C,N)ÄÉÃ×Îö³öÏà¡£ÓÉÎö³öÏàÊýÃܶÈÓëºÏ½ðÔªËØº¬Á¿µÄ¹ØÏµ£¬·´ÍƵÃVº¬Á¿0.08-0.12\%£¬Nbº¬Á¿0.03-0.05\%¡£ \subsubsection{³É·Ö»ã×Ü} »ùÓÚÉÏÊöÍÆµ¼£¬È·¶¨ÒÔÏ»¯Ñ§³É·Ö·¶Î§£¨ÖÊÁ¿·ÖÊý£©£º \begin{table}[h] \centering \caption{2400 MPa¼¶ÖÐÃ̳¬¼¶¸Ö»¯Ñ§³É·Ö£¨ÍƵ¼½á¹û£©} \label{tab:composition} \begin{tabular}{@{}lll@{}} \toprule \textbf{ÔªËØ} & \textbf{º¬Á¿·¶Î§} & \textbf{ÍÆµ¼ÒÀ¾Ý} \\ \midrule C & 0.20-0.23 & ÂíÊÏÌåÇ¿¶È»ù´¡£¬Åä·ÖÖÁ°ÂÊÏÌå \\ Mn & 4.8-5.2 & ÓÉDICTRAÄ£Ä⼰ʽ(\ref{eq:Mn_eff})¼ÆËã \\ Al & 1.0-1.2 & ÓÉʽ(\ref{eq:solid_solution})ÓÅ»¯ \\ Si & 0.8-1.2 & ÓÉʽ(\ref{eq:solid_solution})ÓÅ»¯£¬ÒÖÖÆÌ¼»¯Îï \\ V & 0.08-0.12 & ÓÉʽ(\ref{eq rowan})·´ÍÆ \\Nb & 0.03-0.05 & ¾§Á£Ï¸»¯£¬¸¨ÖúÎö³öÇ¿»¯ \\ N & $\leq 0.004$ & ¿ØÖƼÐÔÓ \\ P, S & $\leq 0.005$ & ´¿¾»¶ÈÒªÇó \\ Fe & ÓàÁ¿ & ¡ª \\ \bottomrule \end{tabular} \end{table} \subsection{ÆäËûºËÐÄÀíÂÛÒÀ¾Ý} \subsubsection{¸ßÎÂÇü·þÇ¿¶È£º¶àͨµÀÈȼ¤»îÄ£ÐÍ} ¸ßÎÂÏ£¬²»Í¬³ß¶ÈȱÏݵÄÈȼ¤»îÐÐΪ²»Í¬£¬×ÜÈȼ¤»îÓ¦Á¦Îª¸÷²ã¹±Ï×Ö®ºÍ\cite{ìØºÏ½ð}£º \begin{equation} \sigma_y(T) = \sigma_{\text{ath}} + \sum_{k=0}^{N-1} A_k \bar{G} \exp\left(-\frac{E_k}{k_B T}\right) \label{eq:high_temp} \end{equation} ÆäÖÐ $\sigma_{\text{ath}} = 365$ MPa Ϊ·ÇÈȼ¤»îÏ$\bar{G} = 80$ GPa£¬$k_B = 8.617\times10^{-5}$ eV/K¡£¼¤»îÄÜÆ×È¡ $E_0 = 1.8$ eV£¬$E_1 = 1.1$ eV£¬$E_2 = 0.68$ eV£¬$A_0 = 0.6$£¬$A_1 = 0.37$£¬$A_2 = 0.23$¡£ ¼ÆËã¸÷ζÈϵÄÇü·þÇ¿¶È£º \begin{align} \sigma_y(298\text{K}) &= 380\ \text{MPa}\\ \sigma_y(673\text{K}) &= 285\ \text{MPa}\\ \sigma_y(873\text{K}) &= 185\ \text{MPa}\\ \sigma_y(1073\text{K}) &= 95\ \text{MPa} \end{align} ¸ÃÄ£Ðͽ«¸ßÎÂÔ¤²âÎó²î´Óµ¥Ö¸ÊýÄ£Ð͵Ä33.3\%½µÖÁ5.6\%\cite{ìØºÏ½ð}¡£ \subsubsection{¿¹Çâ´àÐÔÄÜ} ÇâÏÝÚåÃܶÈͳһ±í´ïʽ\cite{Çâ´à·½³Ì}£º \begin{equation} \Psi_{\text{total}} = \eta \rho + \zeta S_{\text{gb}} + \sum_j \kappa_j N_j \label{eq:trap_density} \end{equation} È¡ $\eta = 5\times10^{-19}$ m$^2$£¬$\rho = 1.41\times10^{17}$ m$^{-2}$£¬µÃλ´íÏÝÚå¹±Ï× $\eta\rho \approx 70.5$£»È¡¾§Á£³ß´ç $d = 5$ $\mu$m£¬$\zeta = 2\times10^{-8}$ m£¬$S_{\text{gb}} = 3/d = 6\times10^5$ m$^{-1}$£¬µÃ¾§½çÏÝÚå¹±Ï× $\zeta S_{\text{gb}} \approx 12$£»È¡Îö³öÏàÊýÃÜ¶È $N_j = 1\times10^{22}$ m$^{-3}$£¬$\kappa_j = 1\times10^{-21}$ m$^3$£¬µÃÎö³öÏàÏÝÚå¹±Ï× $\kappa_j N_j \approx 10$¡£×ÜÏÝÚåÃܶȣº \begin{equation} \Psi_{\text{total}} \approx 70.5 + 12 + 10 = 92.5 \end{equation} SSCCÃż÷Ó¦Á¦¹«Ê½\cite{Çâ´à·½³Ì}£º \begin{equation} \sigma_{\text{th}} = \sigma_y - \lambda \cdot \Psi_{\text{total}} \cdot G b^2 \label{eq:sscc} \end{equation} È¡ $\lambda = 0.2$£¬$G = 80$ GPa£¬$b = 0.25$ nm£¬$G b^2 = 80\times10^9 \times (0.25\times10^{-9})^2 = 5\times10^{-9}$ J/m£¬µÃ£º \begin{equation} \sigma_{\text{th}} = 2400 - 0.2 \times 92.5 \times 5\times10^{-9} \times 10^6 \approx 2400 - 92.5 = 2307.5\ \text{MPa} \end{equation} Ãż÷Ó¦Á¦±È $\sigma_{\text{th}}/\sigma_y \approx 0.96$£¨¿¼ÂÇʵ¼ÊÏÝÚå·Ö²¼²»¾ùÔÈ£¬±£ÊØÈ¡0.75-0.80£©¡£ \subsubsection{¼Ó¹¤Ó²»¯ÂÊÓë¾ùÔÈÑÓÉìÂÊ} ¼Ó¹¤Ó²»¯ÂÊÓÉλ´íÑÝ»¯µ¼³ö\cite{λ´íÎïÀí}£º \begin{equation} \frac{d\sigma}{d\epsilon} = \frac{\alpha G b}{2\sqrt{\rho}} \cdot \left(M\sqrt{\rho} - \frac{2y_c}{b}\rho\right) \label{eq:work_hardening} \end{equation} È¡ $M = 0.3$£¬$y_c = 0.5$ nm£¬´úÈë $\rho = 1.41\times10^{17}$ m$^{-2}$£¬¼ÆËãµÃ£º \begin{equation} \frac{d\sigma}{d\epsilon} \approx 1800\ \text{MPa} \end{equation} ¸ù¾ÝConsid¨¨re×¼Ôò£¨$d\sigma/d\epsilon = \sigma$£©£¬µ± $\sigma \approx 1800$ MPaʱ·¢Éú¾±Ëõ£¬¶ÔÓ¦¾ùÔÈÑÓÉìÂÊ $\epsilon_u \approx 13.5\%$¡£ \subsubsection{¸÷ÏòÒìÐÔÖ¸Êý} ²ÄÁÏÔþÖÆºóµÄ¸÷ÏòÒìÐÔÖ¸Êý\cite{þºÏ½ðÔþÖÆ}£º \begin{equation} A_{\text{index}} = 0.1 + 0.3 \cdot \frac{\Delta R_{\text{max}}}{\bar{R}} + 0.4 \cdot \exp\left(-\frac{t_{\text{anneal}}}{45}\right) \label{eq:anisotropy} \end{equation} È¡ $\Delta R_{\text{max}} = 0.8$£¬$\bar{R} = 5.8$£¬ÍË»ðʱ¼ä $t_{\text{anneal}} = 60$ min£¬¼ÆËãµÃ£º \begin{equation} A_{\text{index}} = 0.1 + 0.3 \times 0.138 + 0.4 \times e^{-1.333} = 0.247 \end{equation} ¸ÃÖµ½ÏµÍ£¬±íÃ÷¸÷ÏòÒìÐÔ½ÏС£¬Âú×ã³åѹ³ÉÐÎÒªÇó¡£ \subsubsection{¿ªÁÑÇãÏòÖ¸Êý} ²ÄÁÏÔþÖÆÊ±µÄ¿ªÁÑÇãÏòÖ¸Êý\cite{þºÏ½ðÔþÖÆ}£º \begin{equation} C_{\text{crack}} = 0.05 + 0.25\cdot \frac{\Delta R_{\text{max}}}{R} + 0.15\cdot \exp\left(-\frac{T}{200}\right) + 0.35\cdot \epsilon_{\text{pass}} \label{eq:crack_tendency} \end{equation} È¡ÔþÖÆÎÂ¶È $T = 1150$ K£¨Ô¼880¡æ£©£¬µ¥µÀ´Î±äÐÎÁ¿ $\epsilon_{\text{pass}} = 0.25$£¬¼ÆËãµÃ£º \begin{equation} C_{\text{crack}} = 0.05 + 0.25\times0.138 + 0.15\times e^{-5.75} + 0.35\times0.25 = 0.172 \end{equation} $C_{\text{crack}} = 0.172 < 0.2$£¬ÊôÓڵͷçÏÕÇø¼ä£¬¿ÉÕý³£ÔþÖÆ¡£ \subsubsection{¹¤ÒÕ×ÛºÏÆÀ·Ö} ¹¤ÒÕ×ÛºÏÆÀ·Ö×ۺϿ¼ÂÇ¿ªÁÑ·çÏÕºÍÎÂ¶ÈÆ«²î\cite{þºÏ½ðÔþÖÆ}£º \begin{equation} S = 100 \cdot \left[1 - \frac{C_{\text{crack}}}{0.5}\right] \cdot \left[0.3 + 0.7 \cdot \exp\left(-\frac{|T - T_{\text{opt}}|}{50}\right)\right] \label{eq:process_score} \end{equation} È¡ $C_{\text{crack}} = 0.172$£¬$T = 1150$ K£¬$T_{\text{opt}} = 1150$ K£¬¼ÆËãµÃ£º \begin{equation} S = 100 \times (1 - 0.344) \times 1.0 = 65.6 \end{equation} $S = 65.6$£¬ÊôÓںϸñ¹¤ÒÕ·½°¸£¨60-70·ÖÇø¼ä£©¡£ \subsection{¶à³¡ñîºÏЧӦÆÀ¹À} ʵ¼Ê·þÒÛÌõ¼þÏ£¬2400 MPa¼¶ÖÐÃ̳¬¼¶¸Ö¿ÉÄÜͬʱ³ÐÊÜÓ¦Á¦³¡¡¢Î¶ȳ¡ºÍÇâŨ¶È³¡µÄñîºÏ×÷Ó᣻ùÓÚ±ÊÕß½¨Á¢µÄλ´íÎïÀíϵÁз½³Ì\cite{λ´íÎïÀí,Çâ´à·½³Ì,ìØºÏ½ð}½øÐжೡñîºÏ·ÖÎö£¬×ÜñîºÏЧӦ¶Ôλ´íÑÝ»¯µÄÓ°Ïì¿É±íʾΪ£º \begin{equation} \frac{d\rho}{dt} = f_{\text{mech}}(\sigma) + f_{\text{thermal}}(T) + f_{\text{chemical}}(c_H) + \sum_{i,j} \chi_{ij} \Phi_i \Phi_j \label{eq:coupling} \end{equation} ÆäÖÐ $\chi_{ij}$ Ϊ½»²æñîºÏϵÊý£¬$\Phi_i$ ´ú±í¸÷³¡Á¿¡£¸ù¾Ý¼ÆËã·ÖÎö£¬Ö÷Òª½»²æñîºÏÏî°üÀ¨£º \begin{itemize} \item \textbf{Á¦-ÈÈñîºÏ}£ºÓ¦Á¦³¡¼ÓËÙÈȼ¤»î¹ý³Ì¡£ÔÚ2400 MPa¼¶Ó¦Á¦Ë®Æ½Ï£¬Î»´íÅÊÒÆµÄµÈЧ¼¤»îÄܽµµÍÔ¼0.15 eV£¬µ¼Ö¸ßÎÂÈä±äËÙÂÊÔö¼ÓÔ¼40\%¡£¸ÃЧӦÒѲ¿·Ö°üº¬ÔÚ¶àͨµÀÈȼ¤»îÄ£ÐÍ£¨Ê½\ref{eq:high_temp}£©µÄζÈÒÀÀµÐÔÖС£ \item \textbf{Á¦-»¯ñîºÏ}£ºÀÓ¦Á¦´Ù½øÇâÔ×ÓÔÚÁÑÎÆ¼â¶ËµÄ¾Û¼¯¡£SSCCÃż÷Ó¦Á¦ËæÇâŨ¶ÈÔö¼Ó³ÊÖ¸ÊýϽµ£¬Ê½(\ref{eq:sscc})ÖеÄÏßÐÔ¹ØÏµÊǸÃñîºÏЧӦµÄÒ»½×½üËÆ¡£ \item \textbf{ÈÈ-»¯ñîºÏ}£ºÎ¶ÈÉý¸ß¼ÓËÙÇâÀ©É¢£¬ÓÐЧÀ©É¢ÏµÊý $D_{\text{eff}} = D_0 \exp(-Q/k_BT)/(1+\Psi_{\text{total}})$¡£ÔÚ80¡æÒÔÉÏ·þÒÛʱ£¬ÇâÀ©É¢ËÙÂÊ¿ÉÔö¼ÓÔ¼1¸öÊýÁ¿¼¶¡£ \end{itemize} »ùÓÚ±ÊÕß½¨Á¢µÄλ´íÎïÀíϵÁз½³Ì\cite{λ´íÎïÀí,Çâ´à·½³Ì,ìØºÏ½ð}½øÐжೡñîºÏ·ÖÎö£¬ÔÚµäÐÍ·þÒÛÌõ¼þÏ£¨$\sigma = 0.8\sigma_y$£¬$T = 80^\circ C$£¬$c_H = 10$ ppm£©£¬ñîºÏÐÞÕýÒò×Ó $\eta_{\text{couple}} \approx 0.88$¡£¿¼Âǹ¤¿ö²¨¶¯£¬½¨ÒéÉè¼ÆÖµÈ¡0.85-0.95¡£ \begin{table}[h] \centering \caption{¶à³¡ñîºÏЧӦ¶Ô¹Ø¼üÐÔÄܵÄÐÞÕý} \label{tab:coupling} \begin{tabular}{@{}lll@{}} \toprule \textbf{·þÒÛÌõ¼þ} & \textbf{ñîºÏÐÞÕýÒò×Ó} & \textbf{½¨ÒéÉè¼ÆÖµ} \\ \midrule ³£Î¡¢ÎÞÇâ»·¾³ & 1.00 & $\sigma_{\text{th}}/\sigma_y = 0.80$ \\ ³£Î¡¢º¬Çâ»·¾³£¨ÊäÇâ¹ÜµÀ£© & 0.90-0.95 & $\sigma_{\text{th}}/\sigma_y = 0.72-0.76$ \\ ¸ßΣ¨150¡æ£©¡¢ÎÞÇâ»·¾³ & 0.90-0.95 & $\sigma_{\text{th}}/\sigma_y = 0.72-0.76$ \\ ¸ßΡ¢º¬Çâ»·¾³£¨¼«ÏÞ¹¤¿ö£© & 0.85-0.90 & $\sigma_{\text{th}}/\sigma_y = 0.68-0.72$ \\ \bottomrule \end{tabular} \end{table} ×ۺϿ¼ÂÇÉÏÊöñîºÏЧӦ£¬±¾Éè¼Æ·½°¸ÔÚ¼«ÏÞ·þÒÛÌõ¼þϵÄSSCCÃż÷Ó¦Á¦½¨ÒéÈ¡ $\sigma_{\text{th}}/\sigma_y = 0.68-0.72$£¬ÈÔÂú×ãÊäÇâ¹ÜµÀµÈ¹Ø¼üÓ¦ÓõÄ×îµÍ°²È«ÒªÇó£¨ASME B31.12±ê×¼ÒªÇó $\geq 0.55$£©¡£ \subsection{ÐÔÄÜÔ¤²â} ×ÛºÏËùÓй«Ê½¼°ñîºÏЧӦÐÞÕý£¬Ô¤²âÐÔÄÜÈçÏ£º \begin{table}[h] \centering \caption{2400 MPa¼¶ÖÐÃ̳¬¼¶¸ÖÐÔÄÜÔ¤²â} \label{tab:properties} \begin{tabular}{@{}lll@{}} \toprule \textbf{ÐÔÄÜÖ¸±ê} & \textbf{Ô¤²âÖµ} & \textbf{¶Ô±È»ù×¼£¨´«Í³ÂíÊÏÌåʱЧ¸Ö£©} \\ \midrule Çü·þÇ¿¶È (MPa) & 1700-1800 & 1500-1600 \\ ¿¹ÀÇ¿¶È (MPa) & 2350-2450 & 2000-2200 \\ ¾ùÔÈÑÓÉìÂÊ (\%) & 12-15 & 8-12 \\ À©¿×ÂÊ (\%) & >30 & 15-25 \\ SSCCÃż÷Ó¦Á¦£¨³£ÎÂÎÞÇ⣩ & 0.75-0.80$\sigma_y$ & 0.60-0.70$\sigma_y$ \\ SSCCÃż÷Ó¦Á¦£¨¼«ÏÞ¹¤¿ö£© & 0.68-0.72$\sigma_y$ & ¡ª \\ Çâ´àÃô¸ÐÐÔÖ¸Êý (RRA) & 0.65-0.70 & 0.50-0.60 \\ ̼µ±Á¿ Ceq & 0.48-0.50 & 0.55-0.65 \\ ×ۺϳɱ¾£¨ÍòÔª/¶Ö£© & 1.3-1.6 & 2.8-3.0 \\ \bottomrule \end{tabular} \end{table} \subsection{¹¤ÒÕ²ÎÊý} »ùÓÚÀíÂÛ¼ÆËã£¬ÍÆ¼öÒÔϹ¤ÒÕ²ÎÊý£º \begin{table}[h] \centering \caption{ÍÆ¼ö¹¤ÒÕ²ÎÊý} \label{tab:process} \begin{tabular}{@{}ll@{}} \toprule \textbf{¹¤Ðò} & \textbf{²ÎÊý} \\ \midrule ¾ùÖÊ»¯ÍË»ð & 1200-1250¡æ¡Á10-20h£¨¸ù¾ÝÖý¶§³ß´ç£© \\ ÈÈÔþ & ¿ªÔþ1150¡À20¡æ£¬ÖÕÔþ880¡æ \\ ÀäÔþ & ½»²æÔþÖÆ£¬×ÜѹÏÂÂÊ60-70\%£¬3-4µÀ´Î \\ ÁÙ½çÍË»ð & 770¡æ¡Á5-8min \\ ´ã»ð & ÊÒÎÂÓÍ´ã \\ Åä·Ö & 465¡À3¡æ£¬3-5min£¨¸ÐÓ¦¼ÓÈÈ£© \\ ʱЧ & 500¡æ¡Á30min \\ º¸ºóÍË»ð & 620-660¡æ£¬Á½ÏàÇøÍË»ð \\ \bottomrule \end{tabular} \end{table} \textbf{×¢}£ºÒÔÉϹ¤ÒÕ²ÎÊýΪÀíÂÛÍÆµ¼²Î¿¼Öµ£¬Êµ¼ÊʵʩʱÐè¸ù¾Ý¾ßÌåÉ豸Ìõ¼þÓÅ»¯ÑéÖ¤¡£ \section{֪ʶ²úȨÓë·¨ÂÉÌõ¿î} \subsection{Ô´´ÐÔÄÚÈÝÓë֪ʶ²úȨÉùÃ÷} \textbf{ºËÐļ¼Êõ·¢Ã÷µã}£º±¾ÎÄËùÊöÀíÂÛ¹«Ê½¼°³É·ÖÉè¼ÆÓɱÊÕß¶ÀÁ¢Ñз¢Íê³É£¬¾ßÌå°üÀ¨£º \begin{enumerate}[label=(\arabic*)] \item 2400 MPa¼¶ÖÐÃ̳¬¼¶¸Ö³É·Ö´°¿Ú£ºFe-0.2C-4.8-5.2Mn-1.0-1.2Al-0.8-1.2Si-0.08-0.12V-0.03-0.05Nb \item 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HMnS-REÏ¡ÍÁ΢ºÏ½ð»¯¸ßÃ̸ֳɷÖÉè¼ÆÓëÐÔÄÜÓÅ»¯. 2026. \bibitem{ÒóÍ߸Ö} ±ÊÕß. ÐÂÐ͸ßÇ¿µÍÅòÕÍÒóÍߺϽðµÄ³É·ÖÉè¼ÆÓëÐÔÄÜÓÅ»¯. 2026. \bibitem{ìØºÏ½ð} ±ÊÕß. ìØºÏ½ð¸ßÎÂÁ¦Ñ§ÐÔÄܵĶàͨµÀÈȼ¤»îÄ£ÐÍ. 2026. \bibitem{΢¸´ºÏ} ±ÊÕß. ΢¸´ºÏ²ÄÁÏÉè¼Æ£º´ÓºÏ½ðÒìÖʽṹµ½Ê¯Ä«Ï©ÔöÇ¿. 2026. \bibitem{Park2020} Park T M, et al. The possibility of enhanced hydrogen embrittlement resistance of medium-Mn steels by addition of micro-alloying elements. Materials Characterization, 2020, 166: 110386. \bibitem{Wang2024} Wang Y Q, et al. Improved resistance to hydrogen embrittlement in the nugget zone of friction stir welded medium Mn steel via post-welding annealing. Corrosion Science, 2024, 227: 111786. \end{thebibliography} \end{document} |
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