From 1a1e774ea12ed90bfb18fc8f2825bee7d6f86a94 Mon Sep 17 00:00:00 2001 From: "Denis V. Dedkov" Date: Thu, 26 Jun 2014 13:31:00 +0600 Subject: [PATCH] Tables was added, figures was added, text of 3 chapter was fixed --- c3.tex | 633 +++++++++++++++++++-------------- common.tex | 2 +- disser.kilepr | 70 ++-- fig/concentrators/p0s0d1d2.png | Bin 0 -> 487273 bytes fig/concentrators/p0s0d3d4.png | Bin 0 -> 431759 bytes fig/concentrators/p0s0d5d6.png | Bin 0 -> 533946 bytes fig/concentrators/p0s0d7.png | Bin 0 -> 117996 bytes fig/concentrators/p0s1d1d2.png | Bin 0 -> 396033 bytes fig/concentrators/p0s1d3d4.png | Bin 0 -> 436887 bytes fig/concentrators/p0s1d5d6.png | Bin 0 -> 525398 bytes fig/concentrators/p0s1d7.png | Bin 0 -> 118293 bytes fig/concentrators/p0s2d1d2.png | Bin 0 -> 304686 bytes fig/concentrators/p0s2d3d4.png | Bin 0 -> 330583 bytes fig/concentrators/p0s2d5d6.png | Bin 0 -> 462580 bytes fig/concentrators/p0s2d7.png | Bin 0 -> 106592 bytes fig/concentrators/p1s0d1d2.png | Bin 0 -> 480201 bytes fig/concentrators/p1s0d3d4.png | Bin 0 -> 432313 bytes 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tables/p2s3.csv create mode 100644 tables/p2s4.csv create mode 100644 tables/p2s5.csv create mode 100644 tables/p3s3.csv create mode 100644 tables/p3s4.csv create mode 100644 tables/p3s5.csv diff --git a/c3.tex b/c3.tex index 871474e..c18860f 100644 --- a/c3.tex +++ b/c3.tex @@ -26,7 +26,7 @@ \newcommand{\kdiagram}[1]{ \begin{tikzpicture} \pgfplotstableread{#1}\loadedtable; -\begin{axis}[xbar stacked, width=10cm,height=10cm, +\begin{axis}[xbar stacked, width=9cm,height=8cm, y dir = reverse, bar width = 0.8, cycle list name=colorbrewer-ylgnbu, @@ -39,7 +39,7 @@ xmin=0, enlarge x limits=false, point meta=explicit, - every node near coord/.append style={font=\small}, + every node near coord/.append style={font=\tiny}, nodes near coords={\pgfmathprintnumber[precision=2, zerofill] {\pgfplotspointmeta}}, nodes near coords align @@ -73,8 +73,7 @@ table[ керамическими волокнами и поликристаллической матрицей при произвольном макродеформировании} -\subsection{Коэффициенты концентрации напряжений при деформации двухстороннего -равнокомпонентного растяжения в плоскости слоя} +% Двухосное равнокомпонентное растяжение Введем безразмерные коэффициенты $K_{\sigma_{ij}} = \sigma_{ij}({\bf r}) / \sigma_{ij}^{per}({\bf r})$, вычисляемые как отношение компонент тензора @@ -83,37 +82,33 @@ table[ Найдем коэффициенты концентрации напряжений в слое тканого композита с керамическими волокнами и поликристаллической матрицей с учетом граничных -условий~\ref{eq:c2:b_cond}, соответствующим деформации двухстороннего +условий~\ref{eq:c2:b_cond}, соответствующих деформации двухстороннего равнокомпонентного растяжения в плоскости слоя. -Максимальные значения коэффициентов концентрации в точке, соответствующей -центру межволоконного пространства для компонент тензора напряжений модели с -гарантированной прослойкой матрицы представлены на -рисунке~\ref{fig:c3:max_k_s0}. +Структура распределения значений коэффициентов концентрации в точке, +соответствующей центру межволоконного пространства для компонент тензора +напряжений модели с гарантированной прослойкой матрицы представлены на +рисунке~\ref{fig:c3:max_k_s0}. Как видим, наибольший вклад в коэффициенты +концентрации всех видов дефектов вносит касательная составляющая тензора +напряжения $\sigma_{13}$. Исключение составляет внутренняя технологическая +пора, которая влияет на коэффициенты концентрации напряжений незначительно. При +наличии локальных технологических дефектов в виде пропуска волокна основы, +разрыва волокна основы или одновременного разрыва волокон основы и утка может +произойти разрушение матрицы по механизмам сдвигов в плоскости слоя. При этом +дополнительные технологические операции по доуплотнению полости, образованной +дефектом, материалом матрицы позволяют снизить влияние концентраторов напряжений +в $1{,}3$ -- $1{,}9$ раза. \begin{figure}[ht!] \centering \kdiagram{tables/p0s0.csv} - \caption{Максимальные коэффициенты концентрации напряжений в центре -межволоконного пространства тканого композита при деформации двухосного -равнокомпонентного растяжении в плоскости слоя} + \caption{Структура значений коэффициентов концентрации напряжений в центре +межволоконного пространства модельного тканого композита с гарантированной +прослойкой матрицы между волокнами при деформации двухосного равнокомпонентного +растяжении в плоскости слоя} \label{fig:c3:max_k_s0} \end{figure} -Как видим, наибольший вклад в коэффициенты концентрации для дефекта, -представляющего собой пропуск волокна основы вносит касательная составляющая -тензора напряжения $\sigma_{23}$. При возникновении такого дефекта как разрыв -волокна основы максимальный вклад вносит нормальная компонента тензора -напряжений $\sigma_{22}$. При одновременном разрыве волокон основы и утка -максимальный вклад вносит касательная компонента тензора напряжений -$\sigma_{13}$. При наличии внутренней технологической поры максимальный вклад -вносит касательная компонента тензора напряжений $\sigma_{12}$. Для всех -дефектов кроме разрыва волокон основы может произойти разрушение матрицы по -механизмам сдвигов в плоскости слоя. Разрыв волокна основы может привести к -расслоению матрицы. При этом дополнительные технологические операции по -доуплотнению полости, образованной дефектом, позволяют снизить влияние -концентраторов напряжений. - На рис.~\ref{fig:c3:k_d1d2_s0}~--~\ref{fig:c3:k_d7_s0} показаны распределения коэффициентов концентрации интенсивностей напряжений в слое тканого композита с искривленными волокнами и поликристаллической матрицей для случая когда @@ -121,15 +116,14 @@ $\sigma_{13}$. При наличии внутренней технологиче типов технологических дефектов и с учётом дополнительной пропитки композита материалом матрицы. Расположение областей, в которых интенсивность напряжений достигает максимальных значений в местах, где искривленные волокна основы или -утка имеют наибольшую кривизну, строго периодично. Исключение составляют -области, расположенные вблизи локальных дефектов, при этом, в случае наличия -дефекта максимальные значения коэффициентов концентрации напряжений приходятся -на фазу тканого наполнителя. При наличии материала матрицы в полостях, -образованных дефектами максимальные значения коэффициентов концентрации -интенсивностей напряжений приходятся на фазу матрицы. +утка имеют наибольшую кривизну, строго периодично, за исключением областей, +расположенные вблизи локальных дефектов. При этом максимальные значения +коэффициентов концентрации напряжений приходятся на фазу матрицы. Наличие +материала матрицы в полостях, образованных дефектами приводит к снижению +коэффициентов концентрации интенсивностей напряжений. \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v1/s0/s0d1d2} + \includegraphics[width=17cm]{concentrators/p0s0d1d2} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с пропуском волокна основы~(а) и с учётом доуплотнения~(б) при деформации двухосного равнокомпонентного растяжения в @@ -138,7 +132,7 @@ $\sigma_{13}$. При наличии внутренней технологиче \end{figure} \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v1/s0/s0d3d4} + \includegraphics[width=17cm]{concentrators/p0s0d3d4} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с разрывом волокна основы~(а) и с учётом доуплотнения~(б) при деформации двухосного равнокомпонентного растяжения в @@ -149,7 +143,7 @@ $\sigma_{13}$. При наличии внутренней технологиче \pagebreak \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v1/s0/s0d5d6} + \includegraphics[width=17cm]{concentrators/p0s0d5d6} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с разрывом волокон основы и утка~(а) и с учётом доуплотнения~(б) при деформации двухосного равнокомпонентного растяжения в @@ -159,43 +153,58 @@ $\sigma_{13}$. При наличии внутренней технологиче \begin{figure}[ht!] \centering - \includegraphics[width=10cm]{concentrators/v1/s0/s0d7} + \includegraphics[width=10cm]{concentrators/p0s0d7} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с внутренней технологической порой при деформации двухосного равнокомпонентного растяжения в плоскости слоя} \label{fig:c3:k_d7_s0} \end{figure} -Структура распределения максимальных значений коэффициентов концентрации -напряжений в точке, соответствующей центру межволоконного пространства, при -условии наличия контакта с трением между волокнами под действием -деформации двухстороннего равнокомпонентного растяжения в плоскости слоя -показана на рис.~\ref{fig:c3:max_k_s0_f}. +% Двухосное равнокомпонентное растяжение с контактом + +Структура распределения значений коэффициентов концентрации напряжений в точке, +соответствующей центру межволоконного пространства, при условии наличия контакта +с трением между волокнами под действием деформации двухстороннего +равнокомпонентного растяжения в плоскости слоя показана на +рис.~\ref{fig:c3:max_k_s0_f}. \begin{figure}[ht!] \centering \kdiagram{tables/p1s0.csv} - \caption{Максимальные коэффициенты концентрации напряжений в центре + \caption{Структура значений коэффициентов концентрации напряжений в центре межволоконного пространства тканого композита при деформации равнокомпонентного -двухосного растяжения в плоскости слоя с контактом между волокнами} +двухосного растяжения в плоскости слоя тканого композита с контактом между +волокнами} \label{fig:c3:max_k_s0_f} \end{figure} Как видим, при наличии контакта с трением между волокнами для всех типов -дефектов наибольший вклад в коэффициенты концентрации вносит нормальная -составляющая тензора напряжений $\sigma_{22}$, что может свидетельствовать о -возможном начале разрушения слоя материала по механизмам расслоения матрицы в -направлении, перпендикулярном плоскости слоя. Дополнительное насыщение полости, -образованной дефектом позволяет снизить коэффициенты концентрации в $1{,}2$ -- -$1{,}6$ раз. +дефектов, кроме пропуска волокна основы наибольший вклад в коэффициенты +концентрации вносит касательная составляющая тензора напряжений $\sigma_{13}$, +что может свидетельствовать о возможном начале разрушения матрицы по +механизмам сдвигов в плоскости слоя. При наличии пропуска волокна основы, +максимальный вклад в коэффициенты концентрации напряжений вносит касательная +составляющая $\sigma_{23}$. Дополнительное насыщение полости, образованной +дефектом материалом матрицы позволяет снизить коэффициенты концентрации в +$1{,}1$ -- $1{,}3$ раза. Распределение коэффициентов концентрации интенсивностей напряжений, вызванных -наличием различных типов дефектов, в слое тканного композита при условии -наличия контакта с трением между волокнами показаны на -рис.~\ref{fig:c3:k_d3d4_s0_f} -- \ref{fig:c3:k_d5d6_s0_f}. +наличием различных типов дефектов в слое тканного композита при условии +наличия контакта с трением между волокнами и деформации двухосного +равнокомпонентного растяжения в плоскоси слоя показаны на +рис.~\ref{fig:c3:k_d1d2_s0_f} -- \ref{fig:c3:k_d5d6_s0_f}. \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v2/scheme1/d1d3} + \includegraphics[width=17cm]{concentrators/p1s0d1d2} + \caption{Распределение коэффициентов концентрации интенсивностей напряжений в +слое тканого композита с пропуском волокна основы~(а) и с учётом +доуплотнения~(б) с контактом между волокнами при деформации двухосного +равнокомпонентного растяжения в плоскости слоя} + \label{fig:c3:k_d1d2_s0_f} +\end{figure} + +\begin{figure}[ht!] + \includegraphics[width=17cm]{concentrators/p1s0d3d4} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с разрывом волокна основы~(а) и с учётом доуплотнения~(б) с контактом между волокнами при деформации двухосного @@ -204,7 +213,7 @@ $1{,}6$ раз. \end{figure} \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v2/scheme1/d2d4} + \includegraphics[width=17cm]{concentrators/p1s0d5d6} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с разрывом волокон основы и утка~(а) и с учётом доуплотнения~(б) с контактом между волокнами при деформации двухосного @@ -212,9 +221,14 @@ $1{,}6$ раз. \label{fig:c3:k_d5d6_s0_f} \end{figure} -% TODO Дописать анализ распределений, заменить рисунки +Как видим, распределение коэффициентов концентрации напряжений строго +периодично, за исключением областей, расположенных вблизи локальных +технологических дефектов. При этом максимальные значения коэффициентов +концентрации интенсивностей напряжений приходятся на фазу тканого наполнителя. +Заполнение полостей, образованных дефектами позволяет снизить значения +коэффициентов концентрации интенсивностей напряжений. -\subsection{Коэффициенты концентрации напряжений при одноосном растяжении} +% Одноосное растяжение Найдем коэффициенты концентрации напряжений в слое тканого композита с керамическими волокнами и поликристаллической матрицей с учетом граничных @@ -233,41 +247,40 @@ $1{,}6$ раз. \label{eq:c3:b_cond:s1} \end{equation} -\noindent соответствующим деформации одноосного растяжения слоя тканого +\noindent соответствующих деформации одноосного растяжения слоя тканого композита в направлении волокон утка. -Максимальные значения коэффициентов концентрации в точке, соответствующей -центру межволоконного пространства для компонент тензора напряжений модели с -гарантированной прослойкой матрицы представлены на +Структура распределения значений коэффициентов концентрации в точке, +соответствующей центру межволоконного пространства для компонент тензора +напряжений модели с гарантированной прослойкой матрицы представлены на рисунке~\ref{fig:c3:max_k_s1}. \begin{figure}[ht!] \centering \kdiagram{tables/p0s1.csv} - \caption{Максимальные коэффициенты концентрации напряжений в центре -межволоконного пространства тканого композита при одноосном растяжении в -направлении волокон основы} + \caption{Структура значений коэффициентов концентрации напряжений в центре +межволоконного пространства тканого композита с гарантированной прослойкой +матрицы между волокнами при одноосном растяжении в направлении волокон основы} \label{fig:c3:max_k_s1} \end{figure} -Можно заметить, что при деформации одностороннего растяжения в направлении +Можно заметить, что при деформации односного растяжения в направлении волокон основы для всех видов дефектов наибольший вклад в коэффициенты -концентраций вносит нормальная составляющая $\sigma_{22}$. Дальнейшее -увеличение нагрузок может привести к расслоению матрицы в направлении, -перпендикулярном плоскости слоя. При этом заполнение полости, образованной -наличием технологического дефекта, материалом матрицы приводит к снижению -коэффициентов концентрации напряжений для всех видов дефектов, исключая пропуск -волокна основы. +концентраций вносит касательная составляющая $\sigma_{13}$. Дальнейшее +увеличение нагрузок может привести к разрушению матрицы по механизмам сдвигов в +слоя. При этом заполнение полости, образованной наличием технологического +дефекта, материалом матрицы приводит к снижению коэффициентов концентрации +напряжений для всех видов дефектов в $1{,}01$ -- $1{,}05$ раза. Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита полотняного плетения с поликристаллической матрицей при наличии различных типов технологических дефектов и с учётом дополнительной -пропитки композита материалом матрицы при деформации одностороннего растяжения +пропитки композита материалом матрицы при деформации одноосного растяжения в направлении волокон основы представлены на рис.~\ref{fig:c3:k_d1d2_s1}~--~\ref{fig:c3:k_d7_s1}. \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v1/s1/s1d1d2} + \includegraphics[width=17cm]{concentrators/p0s1d1d2} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с пропуском волокна основы~(а) и с учётом доуплотнения~(б) при одноосном растяжении в направлении волокон основы} @@ -275,7 +288,7 @@ $1{,}6$ раз. \end{figure} \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v1/s1/s1d3d4} + \includegraphics[width=17cm]{concentrators/p0s1d3d4} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с разрывом волокна основы~(а) и с учётом доуплотнения~(б) при одноосном растяжении в направлении волокон основы} @@ -285,7 +298,7 @@ $1{,}6$ раз. \pagebreak \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v1/s1/s1d5d6} + \includegraphics[width=17cm]{concentrators/p0s1d5d6} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с разрывом волокон основы и утка~(а) и с учётом доуплотнения~(б) при одноосном растяжении в направлении волокон основы} @@ -294,49 +307,48 @@ $1{,}6$ раз. \begin{figure}[ht!] \centering - \includegraphics[width=10cm]{concentrators/v1/s1/s1d7} + \includegraphics[width=10cm]{concentrators/p0s1d7} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с внутренней технологической порой при одноосном растяжении в направлении волокон основы} - \label{fig:c3:k_d7_s3} + \label{fig:c3:k_d7_s1} \end{figure} Как видим, максимальных значений коэффициенты концентрации интенсивностей -напряжений достигают вблизи локальных дефектов. При этом, в случае наличия -локального дефекта в виде пропуска волокна основы, максимальные значения -коэффициентов концентрации интенсивностей напряжений приходятся на фазу матрицы -слоя тканого композита, в то время как для остальных видов дефектов, +напряжений достигают вблизи локальных дефектов. При этом, для всех видов +дефектов, за исключением одновременного разрыва волокон основы и утка, максимальные значения коэффициентов концентрации интенсивностей напряжений -приходятся на фазу волокон. Для всех видов дефектов дополнительное уплотнений -полостей, образованных дефектом материалом матрицы приводит к уменьшению -коэффициентов концентрации интенсивностей напряжений. +приходятся на фазу матрицы слоя тканого композита. В случае одновременно +разрыва волокон основы и утка, максимальные значения коэффициентов концентрации +интенсивностей напряжений приходятся на фазу тканого наполнителя. Для всех +видов дефектов дополнительное уплотнений полостей, образованных дефектом +материалом матрицы приводит к уменьшению коэффициентов концентрации +интенсивностей напряжений. -Структура распределения максимальных значений коэффициентов концентрации -напряжений в точке, соответствующей центру межволоконного пространства, при -условии наличия контакта с трением между волокнами под действием -деформации одностороннего растяжения в направлении волокон основы показана на -рис.~\ref{fig:c3:max_k_s1_f}. Максимальный вклад в коэффициенты концентраций -вносит нормальная составляющая тензора напряжений $\sigma_{22}$, что -говорит о возможном расслоении матрицы в направлении, перпендикулярном -плоскости слоя. При этом дополнительное уплотнение полостей, образованных -дефектом материалом матрицы уменьшает значения коэффициентов концентрации -напряжений в $1{,}8$ раза. +% Одноосное растяжение с контактом + +Структура распределения значений коэффициентов концентрации напряжений в точке, +соответствующей центру межволоконного пространства, при условии наличия контакта +с трением между волокнами под действием деформации одностороннего растяжения в +направлении волокон основы показана на рис.~\ref{fig:c3:max_k_s1_f}. \begin{figure}[ht!] \centering \kdiagram{tables/p1s1.csv} - \caption{Максимальные коэффициенты концентрации напряжений в центре + \caption{Структура значений коэффициентов концентрации напряжений в центре межволоконного пространства тканого композита с контактом между волокнами при одноосном растяжении в направлении волокон основы} \label{fig:c3:max_k_s1_f} \end{figure} -Распределение коэффициентов концентрации интенсивностей напряжений, вызванные -наличием разрыва волокна основы и разрывов волокон основы и утка, показаны на -рис.~\ref{fig:c3:k_d1d2_s1_f} и \ref{fig:c3:k_d3d4_s1_f}. +Максимальный вклад в коэффициенты концентраций вносит кастательная составляющая +тензора напряжений $\sigma_{13}$, что говорит о возможном разрушении матрицы по +механизмам сдвигов в плоскости слоя. При этом дополнительное уплотнение +полостей, образованных дефектом материалом матрицы уменьшает значения +коэффициентов концентрации напряжений в $1{,}01$ -- $1{,}29$ раза. \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v2/scheme3/d1d3} + \includegraphics[width=17cm]{concentrators/p1s1d1d2} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с разрывом волокна основы~(а) и с учётом доуплотнения~(б) с контактом между волокнами при одноосном растяжении в @@ -345,27 +357,38 @@ $1{,}6$ раз. \end{figure} \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v2/scheme3/d2d4} + \includegraphics[width=17cm]{concentrators/p1s1d3d4} + \caption{Распределение коэффициентов концентрации интенсивностей напряжений в +слое тканого композита с разрывом волокна основы~(а) и с учётом +доуплотнения~(б) с контактом между волокнами при одноосном растяжении в +направлении волокон основы} + \label{fig:c3:k_d3d4_s1_f} +\end{figure} + +\begin{figure}[ht!] + \includegraphics[width=17cm]{concentrators/p1s1d5d6} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с разрывом волокон основы и утка~(а) и с учётом доуплотнения~(б) с контактом между волокнами при одноосном растяжении в направлении волокон основы} - \label{fig:c3:k_d3d4_s3_f} + \label{fig:c3:k_d5d6_s1_f} \end{figure} -Максимальных значений коэффициенты концентрации достигают в местах вблизи -локльных дефектов. Для материала с локальным разрывом волокна основы значения -коэффициентов концентрации интенсивностей напряжений достигают $2{,}3$, а при -одновременном разрыве волокон основы и утка --- $2{,}5$, причем заполнение -поры, образовавшейся вследствие наличия локального дефекта, материалом -поликристаллической матрицы, путем дополнительной пропитки конструкции или -осаждения матрицы из газовой фазы, приводит к увеличению коэффициентов -концентрации до $2{,}6$ и $3{,}7$ для случаев разрыва волокна основы и -одновременного разрыва волокон основы и утка соответственно. +Распределение коэффициентов концентрации интенсивностей напряжений в слое +модельного тканого композита при наличии контакта с трением между волокнами, +вызванные различными видами локальных технологических дефектов, показаны на +рис.~\ref{fig:c3:k_d1d2_s1_f}~--~\ref{fig:c3:k_d5d6_s1_f}. Максимальных +значений коэффициенты концентрации достигают в местах вблизи локльных дефектов. +Для модельного слоя тканого композита с пропуском волокна основы влияние +коэффициентов концентрации интенсивностей напряжений незначительны. Для всех +остальных видов дефектов максимальных значений коэффициенты концентрации +интенсивностей напряжений достигают в областях вблизи технологических дефектов +и приходятся на фазу тканого наполнителя. При этом дополнительное насыщение +полостей, образованных локальными технологическими дефектами, материалом +матрицы приводит к снижению коэффициентов концентрации интенсивностей +напряжений. - -\subsection{Коэффициенты концентрации напряжений при деформации чистого -формоизменения} +% Чистое формоизменение Найдем коэффициенты концентрации напряжений в слое тканого композита с керамическими волокнами и поликристаллической матрицей с учетом граничных @@ -384,235 +407,297 @@ $1{,}6$ раз. \label{eq:c3:b_cond:s2} \end{equation} -\noindent соответствующим деформации чистого формоизменения. +\noindent соответствующих деформации чистого формоизменения. -Максимальные значения коэффициентов концентрации напряжений в слое тканного -композита с искривленными волокнами и поликристаллической матрицей при наличии -различных технологических дефектов под воздействием сдвиговых -нагрузок представлены в таблице~\ref{fig:c3:max_k_s2}: +Структура распределения значений коэффициентов концентрации напряжений в точке, +соответствующей центру межволоконного пространства в слое тканного композита с +искривленными волокнами и поликристаллической матрицей при наличии +гарантированной прослойки матрицы между волокнами и с наличием различных видов +технологических дефектов под воздействием деформации чистого +формоизменения представлены в таблице~\ref{fig:c3:max_k_s2}. \begin{figure}[ht!] \centering \kdiagram{tables/p0s2.csv} - \caption{Максимальные коэффициенты концентрации напряжений в центре + \caption{Структура значений коэффициентов концентрации напряжений в центре межволоконного пространства тканого композита при чистом формоизменении} \label{fig:c3:max_k_s2} \end{figure} -Из таблицы видно, что в случае приложения сдвиговых нагрузок к -фрагменту композита с локальными технологическими дефектами максимальные -значения принимают коэффициенты концентрации касательной составляющей -$\sigma_{13}$ и нормальной составляющей $\sigma_{33}$ компонент тензор -напряжений. Для фрагмента с внутренней технологической порой максимальный вклад -в коэффициенты концентрации напряжений вносят касательные составляющие -$\sigma_{12}$ и $\sigma_{23}$ и нормальная составляющая $\sigma_{33}$ тензора -напряжений. +Как видим, в случае деформации чистого формоизменения слоя тканого композита с +локальными технологическими дефектами максимальные вклад в коэффициенты +концентрации напряжений вносят нормальные составляющие тензора напряжений +$\sigma_{22}$ и $\sigma_{33}$, что говорит о том, что при дальнейшем увеличении +нагрузок возможно расслоение матрицы материала в направлении, перпендикулярном +плоскости слоя или разрыв матрицы в направлении волокон утка. Дополнительное +насышение полости, образованной дефектом, материалом матрицы снижает значения +коэффициентов концентрации напряжений в $1{,}02$ -- $1{,}65$ раза. -На рис.~\ref{fig:k_d1d2_s2}~--~\ref{fig:k_d5_s2} показаны распределения +На рис.~\ref{fig:c3:k_d1d2_s2}~--~\ref{fig:c3:k_d7_s2} показаны распределения коэффициентов концентрации интенсивностей напряжений в слое тканого композита с искривленными волокнами и поликристаллической матрицей при наличии различных типов технологических дефектов и с учётом дополнительной пропитки композита материалом матрицы под воздействием сдвиговых нагрузок. \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v1/s1/s1d1d2} + \includegraphics[width=17cm]{concentrators/p0s2d1d2} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с пропуском волокна основы~(а) и с учётом доуплотнения~(б) при чистом сдвиге} - \label{fig:k_d1d2_s2} + \label{fig:c3:k_d1d2_s2} \end{figure} \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v1/s1/s1d3d4} + \includegraphics[width=17cm]{concentrators/p0s2d3d4} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с разрывом волокна основы~(а) и с учётом доуплотнения~(б) при чистом сдвиге} - \label{fig:k_d3d6_s2} + \label{fig:c3:k_d3d4_s2} \end{figure} \pagebreak \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v1/s1/s1d5d6} + \includegraphics[width=17cm]{concentrators/p0s2d5d6} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с разрывом волокон основы и утка~(а) и с учётом доуплотнения~(б) при чистом сдвиге} - \label{fig:k_d4d7_s2} + \label{fig:c3:k_d5d6_s2} \end{figure} \begin{figure}[ht!] \centering - \includegraphics[width=10cm]{concentrators/v1/s1/s1d7} + \includegraphics[width=10cm]{concentrators/p0s2d7} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с внутренней технологической порой при чистом сдвиге} - \label{fig:k_d5_s2} + \label{fig:c3:k_d7_s2} \end{figure} -Вблизи локальных дефектов интенсивности напряжений превышают соответствующие -интенсивности напряжений определенное для композита идеальной периодической -структуры в $1{,}2$ раза при наличии внутренней технологической поры, в $1{,}3$ -раза для случая пропуска или разрыва волокна основы и в $1{,}6$ раз для -одновременного разрыва волокон основы и утка. При этом, в случае разрыва волокна -основы или волокон основы и утка, значение коэффициентов концентрации -интенсивностей напряжений может быть снижено до $1{,}2$ и $1{,}5$ -соответственно, с помощью дополнительных операций доуплотнения -поликристаллической матрицы. +Максимальных значений коэффициенты концентрации интенсивностей напряжений +достигают в обласях, находящихся вблизи локальных технологических дефектов и +приходятся на фазу матрицы для всех видов дефектов, кроме одновременного +разрыва волокон основы и утка. В случае разрыва волокон основы и утка, +максимальные значения коэффициентов концентрации напряжений приходятся на фазу +тканого наполнителя. Дополнительное насыщение полости, образованной дефектом, +материалом матрицы позволяет снизить значения коэффициентов концентрации +интенсивностей напряжений для всех видов дефектов. + +% Чистое формоизменение с контактом + +Структура распределения значений коэффициентов концентрации напряжений в +модельном слое тканого композита при наличии контакта с трением между волокнами +под действием деформации чистого формоизменения представлены на +рис.~\ref{fig:c3:max_k_s2_f}. Как видим, наибольший вклад в коэффициенты +концентрации напряжений вносит касательная составляющая $\sigma_{13}$ тензора +напряжений. Это говорит о возможном разрушении матрицы по механизмам сдвигов в +плоскости слоя. Дополнительное насыщение полости, образованной дефектом +материалом матрицы позволяет снизить коэффициенты концентрации напряжений в +$1{,}02$ -- $1{,}06$ раза. + +\begin{figure}[ht!] + \centering + \kdiagram{tables/p1s2.csv} + \caption{Структура значений коэффициентов концентрации напряжений в центре +межволоконного пространства модельного тканого композита с контактом между +волокнами при чистом формоизменении} + \label{fig:c3:max_k_s2_f} +\end{figure} + +На рис.~\ref{fig:c3:k_d1d2_s2_f} и \ref{fig:c3:k_d5d6_s2_f} представлены +распределения коэффициентов концентрации интенсивностей напряжений, вызванных +наличием дефекта в виде разрыва волокна основы и разрыва волокон основы и утка в +слое модельного тканого композита с поликристаллической матрицей и наличием +контакта с трением между волокнами при чистом сдвиге. + +\begin{figure}[ht!] + \includegraphics[width=17cm]{concentrators/p1s2d1d2} + \caption{Распределение коэффициентов концентрации интенсивностей напряжений в +слое тканого композита с пропуском волокна основы~(а) и с учётом +доуплотнения~(б) с контактом между волокнами при чистом сдвиге} + \label{fig:c3:k_d1d2_s2_f} +\end{figure} + +\begin{figure}[ht!] + \includegraphics[width=17cm]{concentrators/p1s2d3d4} + \caption{Распределение коэффициентов концентрации интенсивностей напряжений в +слое тканого композита с разрывом волокна основы~(а) и с учётом +доуплотнения~(б) с контактом между волокнами при чистом сдвиге} + \label{fig:c3:k_d3d4_s2_f} +\end{figure} + +\clearpage + +\begin{figure}[ht!] + \includegraphics[width=17cm]{concentrators/p1s2d5d6} + \caption{Распределение коэффициентов концентрации интенсивностей напряжений в +слое тканого композита с разрывом волокон основы и утка~(а) и с учётом +доуплотнения~(б) с контактом между волокнами при чистом сдвиге} + \label{fig:c3:k_d5d6_s2_f} +\end{figure} + +Как видим, пропуск волокна основы оказывает незначительное влияние на значения +коэффициентов концентрации интенсивностей напряжений. Для остальных видов +локальных технологических дефектов максимальные значения коэффициентов +концентрации напряжений расположены в областях, находящихся вблизи дефекта и +приходятся на фазу матрицы. Дополнительное насыщение полости, образованной +дефектом материалом матрицы позволяет снизить значения коэффициентов +концентрации интенсивностей напряжений. + +\clearpage \section{Коэффициенты концентрации напряжений в слое тканого композита c металлическими волокнами и поликристаллической матрицей при произвольном макродеформировании} -\subsection{Геометрическая модель слоя тканого композита с контактом между -волокнами} +% Двухстороннее равнокомпонентное сжатие -В качестве дефектов, вызывающих концентрации напряжений будем рассматривать -типичные дефекты, возникающие вследствие очень плотного расположения волокон ---- разрыв волокна основы (рис.~\ref{fig:c3:d1d3}~а) и разрывы волокон основы и -утка (рис.~\ref{fig:c3:d2d4}~а). Кроме того рассмотрим случаи когда пора в -матрице, образованная дефектом заполняется материалом матрицы в ходе -дополнительных технологических операций (рис.~\ref{fig:c3:d1d3}~б и -\ref{fig:c3:d2d4}~б). +Рассмотрим материал из ткани с металлическими волокнами в поликристаллической +матрице. Такие материалы имеют хорошие показатели при сжатии в плоскости слоя. +Найдем коэффициенты концентрации в слое тканого композита с гарантированной +прослойкой матрицы между волокнами, вызванные наличием локльных технологических +дефектов с учетом граничных условий~\ref{eq:c3:b_cond:s3}: -\begin{figure} - \includegraphics[width=17cm]{geometry/v2/d1d3} - \caption{Разрыв волокна основы в тканом композите с поликристаллической -матрицей при наличии контакта между волокнами~(а) с дополнительной -пропиткой~(б)} - \label{fig:c3:d1d3} -\end{figure} +\begin{equation} + \begin{array}{c} + u_1 {\bf (r)}|_{\Gamma_2} = -u_1^0, \quad + u_3 {\bf (r)}|_{\Gamma_1} = -u_1^0, \\ + u_1 {\bf (r)}|_{\Gamma_4} = u_3 {\bf (r)}|_{\Gamma_3} = u_2 + {\bf (r)}|_{\Gamma_5} = u_2 {\bf (r)}|_{\Gamma_6} = 0, \\ + \sigma_{12} {\bf (r)}|_{\Gamma_4} = \sigma_{13} {\bf (r)}|_{\Gamma_4} = + \sigma_{13} {\bf (r)}|_{\Gamma_3} = \sigma_{23} {\bf (r)}|_{\Gamma_3} = 0, \\ + \sigma_{12} {\bf (r)}|_{\Gamma_5} = \sigma_{13} {\bf (r)}|_{\Gamma_5} = + \sigma_{12} {\bf (r)}|_{\Gamma_6} = \sigma_{13} {\bf (r)}|_{\Gamma_6} = 0, + \end{array} + \label{eq:c3:b_cond:s3} +\end{equation} -\begin{figure} - \includegraphics[width=17cm]{geometry/v2/d2d4} - \caption{Разрыв волокон основы и утка в тканом композите с поликристаллической -матрицей при наличии контакта между волокнами~(а) с дополнительной -пропиткой~(б)} - \label{fig:c3:d2d4} -\end{figure} +\noindent соответствующих деформации двухосного равнокомпонентного сжатия +фрагмента модельного тканого композита в плоскости слоя. -\subsection{Численное решение краевой задачи упругости} - -Матрицу будем разбивать 14-узловыми тетраэдральными элементами, а волокно --- -20-узловыми гексаэдральными -элементами. Степень дискретизации -конечно-элементной сетки будем выбирать таким образом, чтобы дальнейшее -уменьшение характерных размеров элементов ни качественно ни количественно не -влияло на значения структурных перемещений, деформаций и напряжений в слое -тканого композита. Параметры сеток, удовлетворяющих этим условиям показаны в -таблице. - -Решив задачу \ref{eq:Eqvilibrium}~--~\ref{eq:Koshi} с граничными условиями -\ref{eq:b_cond}~--~\ref{eq:b_cond_Colomb_2} методом конечных элементов получим -поля интенсивностей напряжений в искривленных нитях основы и утка слоя -модельного тканого композита идеальной периодической структуры, показанных -на рис.~\ref{fig:c3:vmis_v2_s1}. Как видим, распределение искомых полей в -рассматриваемом случае удовлетворяет условиям симметрии и периодичности -геометрической модели и приложенной внешней нагрузке. Это свидетельствует о -корректно построенной модели и корректности полученного численного решения. -Кроме того, обращает на себя внимание концентрация напряжений в местах, где -искривленные нити основы и утка имеют наибольшую кривизну. - -В табл. \ref{fig:c3:max_k_s1_f} представлены максимальные безразмерные -коэффициенты $K_{\sigma_{ij}} = \sigma_{ij}({\bf r}) / -\sigma_{ij}^{per}({\bf r})$, определяемые отношением компонент тензора -напряжений в слое модельного тканого композита с локальным дефектом к -соответствующим компонентам в слое материала идеальной периодической -структуры. Обратим внимание на то, что наибольший вклад в коэффициенты -концентрации вносят касательные составляющие тензора напряжений $\sigma_{13}$. -Напряжения для этих компонент, в 10--48 раз превышают соответствующие значения -для модельного материала с идеальной периодической структурой. - -\begin{figure}[t!] - \centering - \includegraphics[width=17cm]{vmis_v2_s1} - \caption{Поля интенсивности напряжений в нитях основы и утка при -равнокомпонентном двухосном растяжении} - \label{fig:c3:vmis_v2_s1} -\end{figure} - -На рис.~\ref{fig:c3:k_d1d3_s1} и \ref{fig:c3:k_d2d4_s1} представлены -распределения коэффициентов концентрации интенсивностей напряжений для -слоя модельного тканого композита с разрывом волокна основы и разрывом волокон -основы и утка. Расположение областей, в которых интенсивность напряжений -достигает максимальных значений в местах, где искривленные волокна основы или -утка имеют наибольшую кривизну, строго периодично. Исключение составляют -области, расположенные вблизи локального разрыва утка или одновременного -разрыва основы и утка, где интенсивность напряжений превышает соответствующее -значение, определенное для композита идеальной периодической структуры в $2{,}1$ -раза. Стоит заметить, что заполнение поры, образовавшейся вследствие дефекта, -материалом поликристаллической матрицы путем дополнительной пропитки или -осаждения матрицы из газовой фазы приводит к увеличению коэффициентов -концентрации интенсивностей напряжений до $2{,}8$, при разрыве волокна основы -(рис.~\ref{fig:c3:k_d1d3_s1}~б) и $3{,}1$ при разрыве волокон основы и утка -одновременно (рис.~\ref{fig:c3:k_d2d4_s1}~б). - -\subsection{Коэффициенты концентрации напряжений в слое тканого композита с -соприкасающимися волокнами при чистом сдвиге} - -Решим задачу \ref{eq:Eqvilibrium}~--~\ref{eq:Guck} с граничными условиями -\ref{eq:b_cond_ideal}~--~\ref{eq:b_cond:s2}, -соответствующими чистому сдвигу, дополненными граничными условиями -\ref{eq:b_cond_Colomb_1} и \ref{eq:b_cond_Colomb_2}, задающими трения между -волокнами основы и утка тканого композита с поликристаллической матрицей. - -Поля интенсивностей напряжений, полученные в результате решения такой задачи, -показанные на рис.~\ref{fig:c3:vmis_v2_s2}, строго периодичны, что говорит о -корректности полученного решения. - -\begin{figure}[ht] - \includegraphics[width=15cm]{vmis_v2_s2} - \caption{Поля интенсивности напряжений в слое тканого композита с идеальной -периодической структурой при чистом формоизменении и наличии контакта между -волокнами основы и утка} - \label{fig:c3:vmis_v2_s2} -\end{figure} - -Максимальные значения коэффициентов концентрации напряжений представлены в -таблице~\ref{fig:c3:max_k_s3_f}. Как видно из таблицы, наибольший вклад в -коэффициенты концентрации напряжений вносят касательная составляющая -$\sigma_{13}$ и нормальная составляющая $\sigma_{33}$ тензора напряжений. -Значения этих составляющих в материале с дефектом в $10$~--~$29$ раз превышают -соответствующие значения в материале с идеальной периодической структуре. +Структура распределения значений коэффициентов концентрации напряжений в точке, +соответствующей центру межволоконного пространства модельного слоя тканого +композита с гарантированной прослойкой матрицы между волокнами под действием +деформации двухосного равнокомпонентного сжатия в плоскости слоя для различных +видов технологических дефектов показана на рис.~\ref{fig:c3:max_k_s3}. Как +видим, максимальный вклад в коэффициенты концентрации интенсивностей напряжений +вносит касательная составляющая тензора напряжений $\sigma_{13}$, что +свидетельтвует о возможном разрушении матрицы по механизмам сдвигов в плоскости +слоя. Дополнительное насыщение полости, образованной дефектом материалом +матрицы позволяет снизить значения коэффициентов концентрации напряжений в +$1{,}06$ -- $1{,}71$ раза. \begin{figure}[ht!] \centering - \kdiagram{tables/p1s2.csv} - \caption{Максимальные коэффициенты концентрации напряжений в центре -межволоконного пространства тканого композита при чистом формоизменении} + \kdiagram{tables/p2s3.csv} + \caption{Структура значений коэффициентов концентрации напряжений в центре +межволоконного пространства модельного тканого композита с гарантированной +прослойкой матрицы между волокнами при деформации двухосного равнокомпонентного +сжатия в плоскости слоя} + \label{fig:c3:max_k_s3} +\end{figure} + +На рис.~\ref{fig:c3:k_d1d2_s3} и \ref{fig:c3:k_d7_s3} представлены +распределения коэффициентов концентрации интенсивностей напряжений для +слоя модельного тканого композита при наличии гарантированной прослойки +матрицы между волокнами с различными видами дефектов. Области, в которых +коэффициенты концентрации напряжений расположены вблизи локальных +технологических дефектов и приходятся на фазу поликристаллической матрицы. +Дополнительное насыщение полостей, образованных дефектами материалом матрицы +позволяет снизить значения коэффициентов концентрации интенсивностей напряжений. + +\begin{figure}[ht!] + \includegraphics[width=17cm]{concentrators/p2s3d1d2} + \caption{Распределение коэффициентов концентрации интенсивностей напряжений в +слое тканого композита с пропуском волокна основы~(а) и с учётом +доуплотнения~(б) при двухосном равнокомпонентном сжатии} + \label{fig:c3:k_d1d2_s3} +\end{figure} + +\begin{figure}[ht!] + \includegraphics[width=17cm]{concentrators/p2s3d3d4} + \caption{Распределение коэффициентов концентрации интенсивностей напряжений в +слое тканого композита с разрывом волокна основы~(а) и с учётом +доуплотнения~(б) при двухосном равнокомпонентном сжатии} + \label{fig:c3:k_d3d4_s3} +\end{figure} + +\pagebreak + +\begin{figure}[ht!] + \includegraphics[width=17cm]{concentrators/p2s3d5d6} + \caption{Распределение коэффициентов концентрации интенсивностей напряжений в +слое тканого композита с разрывом волокон основы и утка~(а) и с учётом +доуплотнения~(б) при двухосном равнокомпонентном сжатии} + \label{fig:c3:k_d5d6_s3} +\end{figure} + +\begin{figure}[ht!] + \centering + \includegraphics[width=10cm]{concentrators/p2s3d7} + \caption{Распределение коэффициентов концентрации интенсивностей напряжений в +слое тканого композита с внутренней технологической порой при двухосном +равнокомпонентном сжатии} + \label{fig:c3:k_d7_s3} +\end{figure} + +% Двухстороннее равнокомпонентное сжатие с контактом + +Структура распределения значений коэффициентов концентрации напряжений в точке, +соответствующей центру межволоконного пространства модельного слоя тканого +композита при наличии контакта с трением между волокнами с различными видами +технологических дефектов при воздействии деформации двухосного +равнокомпонентного сжатия представлена на рис.~\ref{fig:c3:max_k_s3_f}. + +\begin{figure}[ht!] + \centering + \kdiagram{tables/p3s3.csv} + \caption{Структура значений коэффициентов концентрации напряжений в центре +межволоконного пространства модельного тканого композита с контактом между +волокнами при деформации двухосного равнокомпонентного сжатия в плоскости слоя} \label{fig:c3:max_k_s3_f} \end{figure} -На рис.~\ref{fig:c3:k_d1d3_s2} и \ref{fig:c3:k_d2d4_s2} представлены -распределения коэффициентов концентрации интенсивностей напряжений, вызванных -наличием дефекта в виде разрыва волокна основы и разрыва волокон основы и утка в -слое тканого композита с поликристаллической матрицей при чистом сдвиге. +Как видим, максимальный вклад в коэффициенты концентрации напряжений вносят +касательные составляющие тензора напряжений $\sigma_{23}$ и $\sigma_{12}$, что +говорит о возможном разрушении матрицы по механизмам сдвигов. Доплонительное +насыщение полостей, образованных дефектами приводит к уменьшению значений +коэффициентов концентрации напряжений в $1{,}06$ -- $1{,}79$ раза. + +Распределение коэффициентов концентрации интенсивностей напряжений в слое +модельного тканого композита при наличии контакта с трением между волокнами, с +различными видами технологических дефектов при деформации двухосного +равнокомпонентного сжатия показаны на +рис.~\ref{fig:c3:k_d1d2_s3_f}~--~\ref{fig:c3:k_d5d6_s3_f}. \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v2/scheme2/d1d3} + \includegraphics[width=17cm]{concentrators/p3s3d1d2} + \caption{Распределение коэффициентов концентрации интенсивностей напряжений в +слое тканого композита с пропуском волокна основы~(а) и с учётом +доуплотнения~(б) с контактом между волокнами при чистом сдвиге} + \label{fig:c3:k_d1d2_s3_f} +\end{figure} + +\begin{figure}[ht!] + \includegraphics[width=17cm]{concentrators/p3s3d3d4} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с разрывом волокна основы~(а) и с учётом -доуплотнения~(б) при чистом сдвиге} - \label{fig:c3:k_d1d3_s2} +доуплотнения~(б) с контактом между волокнами при чистом сдвиге} + \label{fig:c3:k_d3d4_s3_f} \end{figure} \begin{figure}[ht!] - \includegraphics[width=17cm]{concentrators/v2/scheme2/d2d4} + \includegraphics[width=17cm]{concentrators/p3s3d5d6} \caption{Распределение коэффициентов концентрации интенсивностей напряжений в слое тканого композита с разрывом волокон основы и утка~(а) и с учётом -доуплотнения~(б) при чистом сдвиге} - \label{fig:c3:k_d2d4_s2} +доуплотнения~(б) с контактом между волокнами при чистом сдвиге} + \label{fig:c3:k_d5d6_s3_f} \end{figure} -Распределение коэффициентов концентрации интенсивностей напряжений строго -периодично и достигает максимальных значений в местах, расположенных вблизи -локальных дефектов. При разрыве волокна основы максимальное значение -коэффициентов концентрации интенсивностей напряжений равно $2{,}3$ -(рис.~\ref{fig:c3:k_d1d3_s2}~а), а при одновременном разрыве волокон основы и -утка --- $3{,}0$ (рис.~\ref{fig:c3:k_d2d4_s2}~б). При этом, заполнение поры, -образовавшейся в результате одновременного разрыва волокон основы и утка, -материалом поликристаллической матрицы путем дополнительной пропитки или -осаждения матрицы из газовой фазы позволяет снизить коэффициенты концентрации -интенсивностей напряжений до $2{,}6$ (рис.~\ref{fig:c3:k_d2d4_s2}~б). - +Максимальных значений коэффициенты концентрации интенсивностей напряжений +достигают в областях, находящихся вблизи локальных технологических дефектов и +приходятся на фазу тканого наполнителя. При этом дополнительное насыщение +полостей, образованных дефектами материалом матрицы снижает значения +коэффициентов концентрации интенсивностей напряжений незначительно. \section*{Выводы к третьей главе} \addcontentsline{toc}{section}{Выводы к третьей главе} diff --git a/common.tex b/common.tex index 7d341c4..69f03b8 100644 --- a/common.tex +++ b/common.tex @@ -146,7 +146,7 @@ SALOME-MECA для определения безразмерного парам $3$ опубликованы в изданиях, входящих в базы цитирования SCOPUS, а $4$ статьи --- в журналах из перечня, рекомендованного ВАК РФ~\citemy{A:bib:dedkov1, A:bib:dedkov2, A:bib:dedkov3} и $15$-и работах в материалах и тезисах -докладов Всероссийских и международных конференций~\citemy{A:bib:dedkov1}. +докладов Всероссийских и международных конференций~\citemy{A:bib:dedkov10}. } \mkcommonsect{contrib}{Личный вклад автора.}{% diff --git a/disser.kilepr b/disser.kilepr index bc43eb5..d3618ee 100644 --- a/disser.kilepr +++ b/disser.kilepr @@ -4,7 +4,7 @@ img_extIsRegExp=false img_extensions=.eps .jpg .jpeg .png .pdf .ps .fig .gif kileprversion=2 kileversion=2.1.3 -lastDocument=c2.tex +lastDocument=my.bib masterDocument= name=disser pkg_extIsRegExp=false @@ -37,7 +37,7 @@ Mode=LaTeX ReadWrite=true [document-settings,item:c2.tex] -Bookmarks=319 +Bookmarks= Encoding=UTF-8 FoldedColumns= FoldedLines= @@ -122,40 +122,40 @@ order=3 [item:c1.tex] archive=true -column=35 +column=8 encoding=UTF-8 highlight=LaTeX -line=1 +line=26 mode=LaTeX open=true order=4 [item:c2.tex] archive=true -column=69 +column=39 encoding=UTF-8 highlight=LaTeX -line=15 +line=123 mode=LaTeX open=true order=5 [item:c3.tex] archive=true -column=7 +column=36 encoding=UTF-8 highlight=LaTeX -line=447 +line=223 mode=LaTeX open=true order=6 [item:common.tex] archive=true -column=56 +column=73 encoding=UTF-8 highlight=LaTeX -line=133 +line=148 mode=LaTeX open=true order=1 @@ -182,12 +182,12 @@ order=7 [item:er.dot] archive=true -column=28 +column=49 encoding=UTF-8 highlight=dot -line=18 +line=7 mode=dot -open=true +open=false order=9 [item:intro.tex] @@ -195,7 +195,7 @@ archive=true column=0 encoding=UTF-8 highlight=LaTeX -line=8 +line=52 mode=LaTeX open=true order=2 @@ -205,7 +205,7 @@ archive=true column=0 encoding=UTF-8 highlight=BibTeX -line=0 +line=35 mode=BibTeX open=true order=8 @@ -215,7 +215,7 @@ archive=true column=0 encoding=UTF-8 highlight=LaTeX -line=14 +line=44 mode=LaTeX open=true order=0 @@ -230,37 +230,37 @@ ViRegisterFlags=0,0 ViRegisterNames=-,^ [view-settings,view=0,item:c1.tex] -CursorColumn=35 -CursorLine=1 +CursorColumn=8 +CursorLine=26 JumpList= -ViMarks=.,1,35,[,1,35,],1,35 +ViMarks=.,26,8,[,26,8,],26,8 ViRegisterContents=ск волокна основы с доуплотнением ,}[ht! 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